cope-01 digital logic
TRANSCRIPT
20
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
20
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
min
term
sSi
mp
lifi e
d m
inte
rms
FF
FF
FF
TF
FT
FT
ab
c/
/
bc
/
FT
TF
TF
FT
ab
c/
/a
b/
TF
TT
ab
c/
/
TT
FT
ab
c/
/
TT
TF
Sum
of m
inte
rms:
q =
a
bc
ab
ca
bc
ab
c/
//
//
//
/0
00
^^
^^
hh
hh
Sum
of s
imp
lifi e
d m
inte
rms:
q =
a
bb
c/
0/
^^
hh
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
16
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
16
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
mon
Boo
lean
ope
rato
rsC
om
mo
nly
use
d o
per
ato
rs o
n e
xpre
ssio
ns
a, b
to d
efi n
e b
oo
lean
alg
ebra
s:
a
b0
(aka
ab
+ o
r “a
OR
b”
or S
UM
)
ab
/
(aka
ab
$ o
r “a
AN
D b
” o
r PR
OD
UC
T)
a (a
ka
aJ
or a
l or “
no
t a ”
)
Oth
er h
and
y o
per
ato
rs:
a
b"
=
ab
0^
h (a
ka “
a IM
PLIE
S b
”) a
b=
^h =
a
ba
b/
0/
^^
hh
(aka
“a
EQU
ALS
b”)
a
b5
=
ab
ab
/0
/^
^h
h (a
ka “
a EX
CLU
SIV
E-O
R b
” o
r “a
XOR
b”)
a
b/
=
ab
0^
h (a
ka “
a N
OT-
AN
D b
”or “
a N
AN
D b
”)
ab
0 =
a
b/
^h
(aka
“a
NO
T-O
R b
”or “
a N
OR
b”)
NA
ND
an
d N
OR
are
the
on
ly s
ole
su
ffi c
ien
t bo
ole
an o
per
ato
rs,
i.e. y
ou
can
red
uce
an
y b
oo
lean
exp
ress
ion
to o
nly
NA
ND
or
on
ly N
OR
op
erat
ors
.
12
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
12
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Axi
omat
ic B
oole
an A
lgeb
ra (
Whi
tehe
ad 1
898)
0
-Law
s/
-Law
sa
a0
= a
aa
/ =
a(r
edu
nd
ant)
ab
0 =
ba
0a
b/
= b
a/
(co
mm
uta
tive
)
ab
c0
0^
h =
ab
c0
0^
ha
bc
//
^h
= a
bc
//
^h
(ass
oci
ativ
e)
aa
b0
/^
h = a
(a
bso
rpti
on
)
ab
c/
0^
h =
ab
ac
/0
/^
^h
h(d
istr
ibu
tio
n)
Tru
ea/
= a
(id
enti
ty)
(co
nst
ant)
aa
0 =
Tru
ea
a/
= F
alse
(in
vers
e)
DeM
org
an
(do
ub
le n
ot)
Nti
lUi
it
Alg
ebra
s al
low
for e
asie
r re
aso
nin
g th
an t
ruth
tab
les.
8
1D
igita
l Log
ic
Uw
e R
. Zim
mer
- T
he A
ustr
alia
n N
atio
nal U
nive
rsity
Co
mp
ute
r Org
anis
atio
n &
Pro
gram
Exe
cuti
on
202
1
21
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
21
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
min
term
sSi
mp
lifi e
d m
inte
rms
FF
FF
FF
TF
FT
FT
ab
c/
/
bc
/
FT
TF
TF
FT
ab
c/
/a
b/
TF
TT
ab
c/
/
TT
FT
ab
c/
/
TT
TF
Sum
of m
inte
rms:
q =
a
bc
ab
ca
bc
ab
c/
//
//
//
/0
00
^^
^^
hh
hh
Sum
of s
imp
lifi e
d m
inte
rms:
q =
a
bb
c/
0/
^^
hh
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
Ever
y co
mb
inat
ion
al fu
nct
ion
can
b
e w
ritt
en a
s a
sum
of p
rodu
cts!
17
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
17
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
All
bina
ry B
oole
an o
pera
tors
Inp
uts
a, b
Fun
ctio
nN
ame
Sum
of p
rod
uct
sN
AN
DD
on
’t ca
res
aF
FT
Tb
uild
,
,x
/0
bF
TF
T
q
FF
FF
Fals
eC
on
stan
t FA
LSE
a, b
FF
FT
ab
/A
ND
ab
ab
//
/
FF
TF
ab
"N
OT-
IMPL
ICA
TIO
Na
b/
^h
FF
TT
aID
ENTI
TY a
bF
TF
Fb
a"
NO
T-IM
PLIC
ATI
ON
a
b/
^h
FT
FT
bID
ENTI
TY b
aF
TT
Fa
b5
EXC
LUSI
VE-
OR
, XO
Ra
ba
b/
0/
^^
hh
FT
TT
ab
0O
Ra
ab
b/
//
TF
FF
ab
0N
OT-
OR
, NO
Ra
b/
^h
TF
FT
ab
=EQ
UA
LITY
, EQ
aa
bb
0/
/^
^h
hT
FT
Fb
INV
ERSE
ba
TF
TT
ba
"IM
PLIC
ATI
ON
ba0
TT
FF
aIN
VER
SE a
aa
/b
TT
FT
ab
"IM
PLIC
ATI
ON
ab
0
TT
TF
ab
/N
OT-
AN
D, N
AN
Da
b0
TT
TT
Tru
eC
on
stan
t Tru
ea,
bO
utp
ut q
13
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
13
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Axi
omat
ic B
oole
an A
lgeb
ra (
Hun
ting
ton
1904
)
0-L
aws
/-L
aws
(red
un
dan
t)
ab
0 =
ba
0a
b/
= b
a/
(co
mm
uta
tive
)
(ass
oci
ativ
e)
(ab
sorp
tio
n)
ab
c0
/^
h =
ab
ac
0/
0^
^h
ha
bc
/0
^h =
a
ba
c/
0/
^^
hh
(dis
trib
uti
on
)
aFa
lse
0 =
aTr
ue
a/
= a
(id
enti
ty)
(co
nst
ant)
aa
0 =
Tru
ea
a/
= F
alse
(in
vers
e)
DeM
org
an
(do
ub
le n
ot)
9
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
9 o
f 481
(cha
pter
1: “
Dig
ital L
ogic
” up
to p
age
96)
Ref
eren
ces
for
this
cha
pter
[Pat
ters
on1
7]D
avid
A. P
atte
rso
n &
Joh
n L
. Hen
nes
syC
om
pu
ter O
rgan
izat
ion
an
d D
esig
n –
Th
e H
ard
war
e/So
ftw
are
Inte
rfac
eA
pp
end
ix A
“Th
e B
asic
s o
f Lo
gic
Des
ign”
AR
M e
dit
ion
, Mo
rgan
Kau
fman
n 2
017
22
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
22
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
FF
FF
FF
TF
FT
FT
FT
TF
TF
FT
TF
TT
TT
FT
TT
TF
18
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
18
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
FF
FF
FF
TF
FT
FT
FT
TF
TF
FT
TF
TT
TT
FT
TT
TF
14
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
14
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Axi
om
atic
Bo
ole
an A
lgeb
ra
… m
any
oth
er a
xio
mat
ic fo
rmu
lati
on
s o
f Bo
ole
an a
lgeb
ra e
xist
.
10
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
10
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
It s
tart
s w
ith
a th
ough
t …
An
Inve
stig
atio
n o
f th
e La
ws
of T
ho
ugh
t o
n W
hic
h a
re F
ou
nd
ed th
e M
ath
emat
ical
Th
eori
es o
f Lo
gic
and
Pro
bab
iliti
es
by
Geo
rge
Boo
le, 1
854
Geo
rge
Bo
ol,
1815
-186
4
23
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
23
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
max
term
sF
FF
Fa
bc
00
FF
TF
ab
c0
0
FT
FT
FT
TF
ab
c0
0
TF
FT
TF
TT
TT
FT
TT
TF
ab
c0
0
max
term
s p
rod
uct
q =
a
bc
ab
ca
bc
ab
c0
0/
00
/0
0/
00
^^
^^
hh
hh
19
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
19
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
min
term
sF
FF
FF
FT
FF
TF
Ta
bc
//
FT
TF
TF
FT
ab
c/
/
TF
TT
ab
c/
/
TT
FT
ab
c/
/
TT
TF
Sum
of m
inte
rms:
q =
a
bc
ab
ca
bc
ab
c/
//
//
//
/0
00
^^
^^
hh
hh
15
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
15
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Red
unda
nt B
oole
an A
lgeb
ra
0-L
aws
/-L
aws
aa
0 =
aa
a/
= a
(red
un
dan
t)
ab
0 =
ba
0a
b/
= b
a/
(co
mm
uta
tive
)
ab
c0
0^
h =
ab
c0
0^
ha
bc
//
^h
= a
bc
//
^h
(ass
oci
ativ
e)
aa
b0
/^
h = a
aa
b/
0^
h = a
(ab
sorp
tio
n)
ab
c0
/^
h =
ab
ac
0/
0^
^h
ha
bc
/0
^h =
a
ba
c/
0/
^^
hh
(dis
trib
uti
on
)
aFa
lse
0 =
aTr
ue
a/
= a
(id
enti
ty)
aTr
ue
0 =
Tru
ea
Fals
e/
= F
alse
(co
nst
ant)
aa
0 =
Tru
ea
a/
= F
alse
(in
vers
e)
ab
0 =
ab
/a
b/
= a
b0
DeM
org
an
a=
a(d
ou
ble
no
t)
(red
un
dan
t)(
dd
t)
… s
eco
nd
nat
ure
for a
co
mp
ute
r sci
enti
st!
11
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
11
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Boo
lean
Val
ues
& O
pera
tors
Ther
e ar
e tw
o v
alu
es:
e.
g. T
rue
and
Fal
se.
(aka
“1”
an
d “
0”)
Two
bin
ary
op
erat
ors
on
exp
ress
ion
s a,
b:
a
b0
(aka
ab
+ o
r “a
OR
b”
or S
UM
)
ab
/
(aka
ab
$ o
r “a
AN
D b
” o
r PR
OD
UC
T)
On
e u
nar
y o
per
ato
r on
an
exp
ress
ion
a:
a
(aka
a
J o
r al o
r “N
OT
a”)
Tru
th ta
ble
s:
ab
ab
0a
b/
aFa
lse
Fals
eFa
lse
Fals
eTr
ue
Tru
eFa
lse
Tru
eFa
lse
Fals
eFa
lse
Tru
eTr
ue
Fals
eTr
ue
Tru
eTr
ue
Tru
e
36
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
36
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Hal
f Add
er
AB
SC
S m
inte
rms
C m
inte
rms
00
00
01
10
AB
/
10
10
AB
/
11
01
AB
/
32
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
32
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Enco
ding
Ass
um
ing
a ty
pe
can
hav
e 7
dif
fere
nt v
alu
es, m
any
form
s o
f en
cod
ing
are
po
ssib
le:
Enu
mer
atio
n ty
pe
Enco
din
g
1-b
it e
rro
r d
etec
tin
g1-
bit
err
or
corr
ecti
ng
Ind
exV
alu
eSi
ngl
e b
itG
ray
cod
eEv
en
par
ity
Ham
min
g (7
,4)
Ham
min
g(3
,1)
Bin
ary
1Se
cure
d00
0000
100
000
0000
0000
000
0000
000
000
2Ta
xi00
0001
000
100
1111
1000
000
0000
111
001
3Ta
ke-o
ff00
0010
001
101
0110
0110
000
0111
000
010
4C
ruis
ing
0001
000
010
0110
0111
100
0001
1111
101
1
5G
lidin
g00
1000
011
010
0101
0101
011
1000
000
100
6A
pp
roac
h01
0000
011
110
1010
1101
011
1000
111
101
7La
nd
ing
1000
000
101
1100
1100
110
1111
1100
011
0
VH
DL
or
Ver
ilog
give
s yo
u fu
ll co
ntr
ol o
ver
the
enco
din
g.
28
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
28
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Th
e lo
gic
equ
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
Min
term
sSi
mp
lifi e
d m
inte
rms
FF
FF
FF
TF
FT
FT
ab
c/
/
bc
/
FT
TF
TF
FT
ab
c/
/a
b/
TF
TT
ab
c/
/
TT
FT
ab
c/
/
TT
TF
Sum
of m
inte
rms:
q =
a
bc
ab
ca
bc
ab
c//
//
//
//
00
0^
^^
^h
hh
hSu
m o
f sim
plifi
ed
min
term
s:q
=
ab
bc
/0
/^
^h
h
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
b/
bh
a b c
ORs
q
ANDs
24
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
24
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
max
term
sSi
mp
lifi e
d m
axte
rms
FF
FF
ab
c00
ab
0F
FT
Fa
bc
00
FT
FT
FT
TF
ab
c00
bc
0
TF
FT
TF
TT
TT
FT
TT
TF
ab
c00
max
term
s p
rod
uct
q =
a
bc
ab
ca
bc
ab
c00
/00
/00
/00
^^
^^
hh
hh
sim
plifi
ed
max
term
s p
rod
uct
q =
a
bb
c0
/0
^^
hh
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
37
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
37
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Hal
f Add
er
AB
SC
S m
inte
rms
C m
inte
rms
00
00
01
10
/
10
10
/
11
01
/
S =
/
0/
^^
hh
C =
/
33
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
33
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Bin
ary
enco
ding
En
cod
ing
of c
ho
ice
if c
om
pac
tnes
s is
ess
enti
al o
r yo
u n
eed
to a
dd
val
ues
.
00
10
10
10 *2
0*2
1*2
2*2
3*2
4*2
5*2
6*2
7
328
2+
+=
42
29
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
29
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Th
e lo
gic
equ
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
Min
term
sSi
mp
lifi e
d m
inte
rms
FF
FF
FF
TF
FT
FT
ab
c//
bc
/
FT
TF
TF
FT
ab
c//
ab
/T
FT
Ta
bc
//
TT
FT
ab
c//
TT
TF
Sum
of m
inte
rms:
q =
a
bc
ab
ca
bc
ab
c//
//
//
//
00
0^
^^
^h
hh
hSu
m o
f sim
plifi
ed
min
term
s:q
=
ab
bc
//
0^
^h
h
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
b/
bh
a b c
ORs
q
ANDs
com
bin
atio
n o
f in
pu
ts,
The
nu
mb
er o
f ter
ms
(“fa
n-i
n” fo
r th
e ga
tes)
in
fl u
ence
s th
e to
tal d
elay
25
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
25
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Lo
gic
is r
edu
cib
le/e
qu
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
max
term
sSi
mp
lifi e
d m
axte
rms
FF
FF
ab
c00
ab
0F
FT
Fa
bc
00
FT
FT
FT
TF
ab
c00
bc
0
TF
FT
TF
TT
TT
FT
TT
TF
ab
c00
max
term
s p
rod
uct
q =
a
bc
ab
ca
bc
ab
c00
/00
/00
/00
^^
^^
hh
hh
sim
plifi
ed
max
term
s p
rod
uct
q =
a
bb
c0
/0
^^
hh
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
Ever
y co
mb
inat
ion
al fu
nct
ion
can
b
e w
ritt
en a
s a
prod
uct
of s
ums!
38
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
38
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Hal
f Add
er
AB
SC
S m
inte
rms
C m
inte
rms
00
00
01
10
/
10
10
/
11
01
/
S =
/
0/
^^
hh =
C =
/
34
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
34
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Bin
ary
enco
ding
En
cod
ing
of c
ho
ice
if c
om
pac
tnes
s is
ess
enti
al o
r yo
u n
eed
to a
dd
val
ues
.
00
10
10
10 *2
0*2
1*2
2*2
3*2
4*2
5*2
6*2
7
328
2+
+=
42
00
00
0=
00
01
1=
00
10
2=
00
11
3=
01
00
4=
01
01
5=
01
10
6=
01
11
7=
10
00
8=
10
01
9=
10
10
A=
10
11
B=
11
00
C=
11
01
D=
11
10
E=
11
11
F=
Bin
ary
Hex
adec
imal
Dec
imal = = = = = = = = = = = = = = = =
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
30
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
30
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Proc
essi
ng D
ata
Encr
ypti
ng
a b
it v
ecto
r (w
hat
ever
it r
epre
sen
ts)
wit
h a
sec
ret k
ey:
Ass
um
ing
the
key
is r
and
om
an
d n
ot u
sed
for
anyt
hin
g el
se:
Th
is is
su
rpri
sin
gly
secu
re
… a
nd
ext
rem
ely
fast
!
D0
XOR
K0
E 0
Encryption
XOR
Decryption
D0
D1
XOR
K1
E 1XO
RD
1
D2
XOR
K2
E 2XO
RD
2
D3
XOR
K3
E 3XO
RD
3
D4
XOR
K4
E 4XO
RD
4
D5
XOR
K5
E 5XO
RD
5
D6
XOR
K6
E 6XO
RD
6
D7
XOR
K7
E 7XO
RD
7
26
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
26
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Dig
ital
Ele
ctro
nics
Sym
bo
lic:
/=
Ele
men
tary
logi
c ga
te s
ymb
ols
:
Dia
gram
:
Tech
no
logy
:
≡
NA
ND
A BQ
A B
Q
PMO
S
NM
OS
NA
ND
NA
ND
NA
ND
AQ
NA
ND
NA
ND
NA
ND
Q
Q
A B A B
NA
ND
NA
ND
NA
ND
NA
ND
A B
Q
NOT
AQ
OR
QA B
QA B
AND
XOR
A BQ
≡ ≡ ≡ ≡
39
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
39
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Hal
f Add
er
AB
SC
S m
inte
rms
C m
inte
rms
00
00
01
10
/
10
10
/
11
01
/
S =
/
0/
^^
hh =
C =
/
AXO
R
AND
B
S C
35
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
35
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Bin
ary
enco
ding
En
cod
ing
of c
ho
ice
if c
om
pac
tnes
s is
ess
enti
al o
r yo
u n
eed
to a
dd
val
ues
.
00
10
10
10 *2
0*2
1*2
2*2
3*2
4*2
5*2
6*2
7
328
2+
+=
42
00
00
0=
00
01
1=
00
10
2=
00
11
3=
01
00
4=
01
01
5=
01
10
6=
01
11
7=
10
00
8=
10
01
9=
10
10
A=
10
11
B=
11
00
C=
11
01
D=
11
10
E=
11
11
F=
Bin
ary
Hex
adec
imal
Dec
imal = = = = = = = = = = = = = = = =
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2A
*160
3210
+=
42
*161
31
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
31
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Bit
Vec
tors
Gro
up
s o
f bit
s co
uld
rep
rese
nt:
Stat
es, e
nu
mer
atio
n v
alu
es, a
rray
s o
f Bo
ole
ans,
nu
mb
ers,
etc
. pp
.…
or
any
gro
up
ing
or
com
bin
atio
n o
f th
e ab
ove
A
lgeb
raic
Typ
es
The
form
of e
nco
din
g co
uld
be
cho
sen
to o
pti
miz
e fo
r:
• Pe
rfor
man
ce
e.g
. min
imal
dec
od
ing
effo
rt
• R
edun
danc
y / e
rro
r d
etec
tio
n
e.g
. lar
ge H
amm
ing
dis
tan
ce
• Sa
fe t
rans
itio
ns
e.g
. Gra
y co
des
• Ph
ysic
al m
appi
ng
e.g
. map
s o
n e
xist
ing
har
dw
are
inte
rfac
es
• C
ompa
ctne
ss
e.g
. ho
lds
the
max
imal
nu
mb
er o
f val
ues
per
mem
ory
cel
l
27
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
27
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Com
bina
tion
al L
ogic
Fun
ctio
ns
Th
e lo
gic
equ
ival
ent t
o p
ure
fun
ctio
ns:
ther
e ar
e n
o s
tate
s!
IF th
e fu
nct
ion
is c
om
bin
atio
nal
then
ther
e is
on
ly o
ne
ou
tpu
t fo
r an
y co
mb
inat
ion
of i
np
uts
, e.
g. th
e fu
nct
ion
can
be
wri
tten
ou
t as
a tr
uth
tab
le:
ab
cO
utp
ut q
Min
term
sSi
mp
lifi e
d m
inte
rms
FF
FF
FF
TF
FT
FT
ab
c//
bc
/
FT
TF
TF
FT
ab
c//
ab
/T
FT
Ta
bc
//
TT
FT
ab
c//
TT
TF
Sum
of m
inte
rms:
q =
a
bc
ab
ca
bc
ab
c//
//
//
//
00
0^
^^
^h
hh
hSu
m o
f sim
plifi
ed
min
term
s:q
=
ab
bc
/0
/^
^h
h
Sim
plifi
cat
ion
s ca
n b
e d
on
e b
y (a
uto
mat
ed) a
lgeb
raic
tran
sfo
rmat
ion
s, K
arn
augh
map
s o
r o
ther
s
b/
bh
a b c
q
ORs
ANDs
52
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
52
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
2’s
com
plem
ents
The
2’s
com
ple
men
t en
cod
ing
inte
rpre
ts
the
nat
ura
l bin
ary
ran
ge 2n
1-
… 2
1n
-
as n
egat
ive
nu
mb
ers
2n1
--
…
1-
00
10
10
10
11
01
01
10
… …000
000000111
000000111
000000111
000……
000111
…111
000000111
000000111
111000000
00
00
00
00
11
11
11
11
0
00
10
10
10
11
01
01
10
…
2n-1 -1
00
00
00
00
01
11
11
11
00
01
01
01
0…
10
00
00
00
-2n-
1
Nat
ural
bin
ary
num
bers
2's
com
plem
ent b
inar
y nu
mbe
rs
2n -1…
48
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
48
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
2 -
1 =
1 ?
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
44
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
44
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Full
Add
er
Ai
BiCi
1-
SiCi
Si m
inte
rms
Ci m
inte
rms
00
00
00
10
10
AB
Ci
ii
1/
/-
10
01
0A
BC
ii
i1
//
-1
10
01
AB
Ci
ii
1/
/-
00
11
0A
BC
ii
i1
//
-0
11
01
AB
Ci
ii
1/
/-
10
10
1A
BC
ii
i1
//
-1
11
11
AB
Ci
ii
1/
/-
AB
Ci
ii
1/
/-
Si =
AB
Ci
ii
15
5-
^h
Ci =
AB
CA
BC
AB
CA
BC
ii
ii
ii
ii
ii
ii
11
11
//
0/
/0
//
0/
/-
--
-_
_^
^i
ih
h=
AB
CA
BC
AB
CA
BC
ii
ii
ii
ii
ii
ii
11
11
//
//
0/
/0
//
0-
--
-_
^_
^i
hi
h=
AB
AB
AB
Ci
ii
ii
ii
1/
0/
//
0-
^___
^h
ih i
i=
AB
AB
Ci
ii
ii
1/
05
/-
^^^
hh
h
40
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
40
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Full
Add
er
Ai
BiCi
1-
SiCi
00
00
00
10
10
10
01
01
10
01
00
11
00
11
01
10
10
11
11
11
53
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
53
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
2’s
com
plem
ents
The
2’s
com
ple
men
t en
cod
ing
inte
rpre
ts
the
nat
ura
l bin
ary
ran
ge 2n
1-
… 2
1n
-
as n
egat
ive
nu
mb
ers
2n1
--
…
1-
00
10
10
10
11
01
01
10
… …000
000000111
000000111
000000111
000…
000111
…111
000000111
000000111
111000000
00
00
00
00
11
11
11
11
0
00
10
10
10
11
01
01
10
…
2n-1 -1
00
00
00
00
01
11
11
11
00
01
01
01
0…
10
00
00
00
-2n-
1
Nat
ural
bin
ary
num
bers
2's
com
plem
ent b
inar
y nu
mbe
rs
2n -1…
It’s
all
in y
ou
r min
d!
49
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
49
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rad
ix c
ompl
emen
ts C
an w
e d
efi n
e n
egat
ive
nu
mb
ers
such
that
ou
r ad
der
sti
ll w
ork
s?
xx
0-
=
Or:
wh
at c
an y
ou
ad
d to
42
in a
n 8
bit
bin
ary
rep
rese
nta
tio
n
such
that
the
resu
lt w
ill b
e 28 (a
nd
hen
ce 0
in 8
bit
s)?
00
10
10
10
??
??
??
??
+ =
00
00
00
00
1
42 -42
256
45
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
45
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Full
Add
er
Ai
BiCi
1-
SiCi
Si m
inte
rms
Ci m
inte
rms
00
00
00
10
10
AB
Ci
ii
1/
/-
10
01
0A
BC
ii
i1
//
-1
10
01
AB
Ci
ii
1/
/-
00
11
0A
BC
ii
i1
//
-0
11
01
AB
Ci
ii
1/
/-
10
10
1A
BC
ii
i1
//
-1
11
11
AB
Ci
ii
1/
/-
AB
Ci
ii
1/
/-
Si =
AB
Ci
ii
15
5-
^h
Ci =
AB
AB
Ci
ii
ii
1/
05
/-
^^^
hh
h
Ai
XOR
AND
Bi
XOR
AND
OR
S i
Ci-
1C
i
41
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
41
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Full
Add
er
Ai
BiCi
1-
SiCi
Si m
inte
rms
Ci m
inte
rms
00
00
00
10
10
AB
Ci
ii
1/
/-
10
01
0A
BC
ii
i1
//
-1
10
01
AB
Ci
ii
1/
/-
00
11
0A
BC
ii
i1
//
-0
11
01
AB
Ci
ii
1/
/-
10
10
1A
BC
ii
i1
//
-1
11
11
AB
Ci
ii
1/
/-
AB
Ci
ii
1/
/-
Si =
AB
CA
BC
AB
CA
BC
ii
ii
ii
ii
ii
ii
11
11
//
0/
/0
//
0/
/-
--
-_
__
^i
ii
h
54
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
54
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
2 -
1 =
1 ?
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
50
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
50
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rad
ix c
ompl
emen
ts C
an w
e d
efi n
e n
egat
ive
nu
mb
ers
such
that
ou
r ad
der
sti
ll w
ork
s?
xx
0-
=
Or:
wh
at c
an y
ou
ad
d to
42
in a
n 8
bit
bin
ary
rep
rese
nta
tio
n
such
that
the
resu
lt w
ill b
e 28 (a
nd
hen
ce 0
in 8
bit
s)?
00
10
10
10
11
01
01
10
+ =
00
00
00
00
1
42 -42
256
46
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
46
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
2 +
2 =
4 ?
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
42
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
42
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Full
Add
er
Ai
BiCi
1-
SiCi
Si m
inte
rms
Ci m
inte
rms
00
00
00
10
10
AB
Ci
ii
1/
/-
10
01
0A
BC
ii
i1
//
-1
10
01
AB
Ci
ii
1/
/-
00
11
0A
BC
ii
i1
//
-0
11
01
AB
Ci
ii
1/
/-
10
10
1A
BC
ii
i1
//
-1
11
11
AB
Ci
ii
1/
/-
AB
Ci
ii
1/
/-
Si =
AB
CA
BC
AB
CA
BC
ii
ii
ii
ii
ii
ii
11
11
//
0/
/0
//
0/
/-
--
-_
__
^i
ii
h=
A
BA
BC
AB
AB
Ci
ii
ii
ii
ii
i1
1/
//
0/
//
00
--
__^
____
^h
iii
ihi
i=
A
BC
AB
Ci
ii
ii
i1
15
/0
/=
--
_ ^^^
hi
hh =
A
BC
AB
Ci
ii
ii
i1
15
/0
/5
--
_ ^__
hi
ii
= A
BC
ii
i1
55
-^
h
55
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
55
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
2 -
1 =
1 !
… w
ith
an
ove
rall
carr
y-fl
ag in
dic
ated
.
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
51
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
51
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rad
ix c
ompl
emen
ts C
an w
e d
efi n
e n
egat
ive
nu
mb
ers
such
that
ou
r ad
der
sti
ll w
ork
s?
xx
0-
=
Or:
wh
at c
an y
ou
ad
d to
42
in a
n 8
bit
bin
ary
rep
rese
nta
tio
n
such
that
the
resu
lt w
ill b
e 28 (a
nd
hen
ce 0
in 8
bit
s)?
00
10
10
10
11
01
01
10
+ =
00
00
00
00
1
42 -42
256
“In
vert
all
bit
s an
d a
dd
1”
2’s-
com
plem
ent
(as
the
rad
ix/b
ase
is 2
)
47
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
47
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
2 +
2 =
4 !
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
43
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
43
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Full
Add
er
Ai
BiCi
1-
SiCi
Si m
inte
rms
Ci m
inte
rms
00
00
00
10
10
AB
Ci
ii
1/
/-
10
01
0A
BC
ii
i1
//
-1
10
01
AB
Ci
ii
1/
/-
00
11
0A
BC
ii
i1
//
-0
11
01
AB
Ci
ii
1/
/-
10
10
1A
BC
ii
i1
//
-1
11
11
AB
Ci
ii
1/
/-
AB
Ci
ii
1/
/-
Si =
AB
Ci
ii
15
5-
^h
Ci =
AB
CA
BC
AB
CA
BC
ii
ii
ii
ii
ii
ii
11
11
//
0/
/0
//
0/
/-
--
-_
_^
^i
ih
h
68
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
68
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Der
ivin
g SR
Flip
Flo
ps
SR
Q m
inte
rms
00
0*
SR
Q/
/
00
1*
SQ
R/
/
01
01
SR
Q/
/
01
11
SR
Q/
/
10
00
10
10
11
00
11
11
SR
Q/
/
64
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
64
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
SR
00
??
01
10
10
01
11
60
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
60
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
SR
00
??
01
??
10
??
11
??
56
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
56
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
How
long
do
es it
tak
e un
til t
he
last
car
ry fl
ag s
tab
ilize
s ?
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
69
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
69
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Der
ivin
g SR
Flip
Flo
ps
SR
Q m
inte
rms
Sim
plifi
ed
00
0*
SR
Q/
/
S0
01
*S
QR
//
01
01
SR
Q/
/
01
11
SR
Q/
/
RQ
/
10
00
10
10
11
00
11
11
SR
Q/
/
Q =
SR
Q0
/^
h
65
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
65
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
NA
ND
NA
ND
≡Q Q
NA
ND
NA
ND
NA
ND
Q
NA
ND
Q
S R
S R
NA
ND
NA
ND
SR
00
½ ½
01
10
10
01
11
Ass
um
ing Q
as
wel
l as Q
to
be
acti
ve s
imu
ltan
eou
sly
may
lead
to in
stab
ility
.
61
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
61
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
SR
00
??
01
??
10
??
11
57
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
57
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Rip
ple
Car
ry A
dder
Wha
t d
isti
ngui
shes
the
red
fro
m t
he g
reen
gat
es ?
A1
XOR
AND
B1
XOR
AND
OR
S 1A
2
XOR
AND
B2
XOR
AND
OR
S 2
C1
C2
A0
XOR
AND
B0
S 0
C0
Car
ry-l
oo
kah
ead
cir
cuit
ry
70
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
70
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Der
ivin
g SR
Flip
Flo
ps
SR
Q m
inte
rms
Sim
plifi
ed
00
0*
SR
Q/
/
S0
01
*S
QR
//
01
01
SR
Q/
/
01
11
SR
Q/
/
RQ
/
10
00
10
10
11
00
11
11
SR
Q/
/
Q =
SR
Q0
/^
h = S
RQ
//
66
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
66
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
SR
00
Forb
idd
en0
11
01
00
11
1Q
Q
“S-R
Flip
-Flo
p”
62
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
62
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
SR
00
??
01
??
10
??
11
58
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
58
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Ari
thm
etic
Log
ic U
nit
(ALU
)
Ai
XOR
AND
Bi
XOR
AND
OR
S i
Ci-
1C
i
AND
AND
AND
AND
OR
OR
OP 1
-4R
esu
lti
AND
AND
AND
AND
OP 1
(AD
D)
OP 2
(XO
R)
OP 3
(AN
D)
OP 4
(OR
)
INST
R
ALU
Slic
e i
ALU
In
stru
ctio
nD
eco
der
A s
imp
le A
LU w
hic
h c
an A
DD
, XO
R, A
ND
, OR
two
arg
um
ents
.
71
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
71
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Der
ivin
g SR
Flip
Flo
ps
SR
Q m
inte
rms
Sim
plifi
ed
00
0*
SR
Q/
/
S0
01
*S
QR
//
01
01
SR
Q/
/
01
11
SR
Q/
/
RQ
/
10
00
10
10
11
00
11
11
SR
Q/
/
Q =
SR
Q0
/^
h = S
RQ
//
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
67
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
67
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Der
ivin
g SR
Flip
Flo
ps
SR
00
0*
00
1*
01
01
01
11
10
00
10
10
11
00
11
11
63
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
63
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Stat
es
≡Q Q
NA
ND
Q
NA
ND
Q
S R
S R
SR
00
??
01
10
10
??
11
59
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
59
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Tow
ards
Sta
tes
(eve
ryth
ing
up
to h
ere
was
co
mb
inat
ion
al lo
gic)
Ho
w d
o w
e m
ake
op
erat
ion
s d
epen
ds
on
:
… a
n o
verfl
ow
in th
e p
revi
ou
s o
per
atio
n?
… th
e st
ate
of t
he
CPU
?
… a
co
un
ter
hav
ing
reac
hed
zer
o?
… tw
o a
rgu
men
ts h
avin
g b
een
eq
ual
?
… e
tc. p
p.
We
nee
d to
ho
ld o
n to
so
me
stat
es!
84
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
84
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Slav
eSl
aM
asMM
as
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C80
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
80
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Slav
eSl
aM
asMM
as
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C76
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
76
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
72
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
72
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
85
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
85
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Mas
MMas
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C
Slav
e fo
llow
s o
n th
e fa
llin
g cl
ock
ed
ge
81
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
81
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Slav
eSl
aM
asMM
as
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C77
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
77
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
73
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
73
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
86
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
86
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Slav
eSl
aM
asMM
as
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C
Slav
e fo
llow
s o
n th
e fa
llin
g cl
ock
ed
geSl
ave
fSl
The
dec
ou
plin
g b
etw
een
th
e tw
o s
tage
s m
akes
this
fl
ip-fl
op
rac
e fr
ee –
eve
n
in JK
-to
ggle
mo
de.
82
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
82
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Slav
eSl
aM
asMM
as
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C78
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
78
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
74
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
74
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
87
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
87
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Reg
iste
r
D0
Q0
D
C
D1
Q1
D
D2
Q2
D
D3
Q3
D
D4
Q4
D
D5
Q5
D
D6
Q6
D
D7
Q7
D
Co
uld
ser
ve a
s a
gen
eric
, fas
t sto
rage
insi
de
the
CPU
(gen
eral
reg
iste
r)
Or
to h
old
inte
rnal
sta
tes
(e.g
. ALU
ove
rfl o
w) o
f th
e C
PU
wh
ich
are
use
d b
y e.
g. b
ran
chin
g in
stru
ctio
ns.
83
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
83
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Mas
ter-
Slav
e JK
Flip
-Flo
p
Mas
ter
Slav
eSl
aM
asMM
as
NA
ND
NA
ND
Q Q
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NOT
S R
J K C
J K
Q Q
S R≡
C
Mas
ter
is r
eset
on
the
risi
ng
clo
ck e
dge
79
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
79
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
75
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
75
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
D F
lip-F
lop
DQ Q≡
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
NA
ND
DC
Q Q
C
S RSet p
re-l
atch
Res
et p
re-l
atch
96
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
96
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Dig
ital
Lo
gic
• B
oole
an A
lgeb
ra
• Tr
uth
tab
les
and
Bo
ole
an o
per
atio
ns
• M
inte
rms
and
sim
plif
yin
g ex
pre
ssio
ns
• C
ombi
nati
onal
Log
ic
• Lo
gic
gate
s
• N
um
ber
s
• A
dd
ers,
ALU
• St
ate-
orie
nted
Log
ic
• Fl
ip-F
lop
s, r
egis
ters
an
d c
ou
nte
rs
• C
PU A
rchi
tect
ure
Sum
mar
y
92
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
92
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
STM
32L4
76 D
isco
very
Mai
n M
CU
Deb
ugg
er M
CU
Dis
pla
y M
CU
88
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
88
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Togg
le F
lip-F
lop
Q Q
DQ Q≡
S R
J K
Q Q
S R
≡S R
J K
Q Q
S R
D CT
Q Q≡
J K
Q Q
S R
T C
TQ Q≡
DQ Q
XOR
T C
JQ Q≡
DQ Q
CK
AND
ORAN
D
J K
S R
S R
Togg
le F
lip-F
lop
s ch
ange
sta
te w
ith
eve
ry c
lock
cyc
le.
93
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
93
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
STM
32L4
76 D
isco
very
Joys
tick
Res
et
OTG
LED
s
Pow
erD
ebu
gger
st
ate
Use
r LE
Ds
Ove
r cu
rren
t
89
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
89
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Cou
nter
TS R
TS R
TS R
TS R
TS R
TS R
TS R
TS R
1
C
S 0S 1
S 2S 3
S 4S 5
S 6S 7
R
Q0
Q1
Q2
Q3
Q4
Q5
Q6
Q7
11
11
11
1
You
r co
ntr
olle
r h
as m
any
cou
nte
rs w
hic
h c
an
e.g.
be
use
d to
del
ay o
per
atio
ns
wit
ho
ut t
he
nee
d to
exe
cute
inst
ruct
ion
s.
94
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
94
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
STM
32L4
76 D
isco
very
Cu
rren
t met
er to
MC
U 6
0 n
A …
50
mA
UR
Zi
Th
Hea
dp
ho
ne
jack
USB
OTG
Mu
ltip
lexe
d 2
4 b
itRD
-DA
Co
nve
rter
wit
h
ster
eo p
ow
er a
mp
Mic
rop
ho
ne
“9 a
xis”
mo
tio
n s
enso
r (u
nd
ern
eath
dis
pla
y):
3 ax
is a
ccel
ero
met
er
3 ax
is g
yro
sco
pe
3 ax
is m
agn
eto
met
er
90
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
90
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
Sim
ple
CPU
Arc
hite
ctur
e
You
can
alr
ead
y b
uild
mo
st o
f th
e co
mp
on
ents
of a
CPU
by
no
w.
(Th
e m
ost
ess
enti
al m
issi
ng
com
po
nen
t is
the
sequ
ence
r w
hic
h is
a s
pec
ializ
ed s
tate
-mac
hin
e.)
We
will
co
me
bac
k to
the
CPU
arc
hit
ectu
res
tow
ard
s th
e en
d o
f th
e co
urs
e.
Th
e n
ext c
hap
ter
will
be
abo
ut
pro
gram
min
g a
CPU
at m
ach
ine
leve
l.
ALU
Memory
Sequ
ence
rD
ecod
er
Cod
e m
anag
emen
t
Reg
iste
rs
IP SP
Flag
s
Dat
a m
anag
emen
t
95
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
95
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
STM
32L4
76 D
isco
very
Ther
e is
a lo
t mo
re h
ard
war
e h
ere
than
yo
u c
ou
ld p
oss
ibly
m
aste
r in
on
e se
mes
ter
…
… a
nd
yo
u w
ill m
aste
r a
lot
mo
re a
bo
ut
CPU
s at
th
e en
d t
he
cou
rse
than
yo
u t
hin
k n
ow
.
91
Dig
ital
Lo
gic
© 2
021
Uw
e R
. Zim
mer
, The
Aus
tral
ian
Nat
iona
l Uni
vers
ity
page
91
of 4
81 (c
hapt
er 1
: “D
igita
l Log
ic”
up to
pag
e 96
)
STM
32L4
76 D
isco
very