the architecture of konrad zuse’s early computers raúl rojas freie universität berlin
Post on 19-Dec-2015
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Topics
•Overview•Arithmetic in the Z1 and Z3•The processor•The datapath•Highlights•Were the Z1 and Z3 universal?
The chronology
•Z1 1936-38•Z2 1939•Z3 1940-41•S1 1942 - „Sondermaschine 1“
•S2 1944 - „Sondermaschine 2“
•Z4 1942-45
The Z1 and Z3
Z1 (1936-1938)
Z3 (1938-1941)
- mechanical design
- programmable (punched tape)
- basic arithmetic operations
- completely binary
- floating-point machine
- built with relays
- logically equivalent to the Z1
The block architecture
Binary memory
64 wordsmantissa
FP processor
exponent
Numerickeyboard
Numericdisplay
control unit
punchedtape
Decimal input = + 13542 10
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
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7
8
9
1
+_
0 6 7 8-8 -7 -6
decimal exponent
sign
decimalmantissa
2
4
5
3
1
+
7
7
•In the Z1 and Z3
•IEEE Standard
Floating-Point Coding
exponent mantissa
+, -
exponent mantissa+, -
1 bit 6 bit 14 bit
1 bit 7 bit 24 bit
Normalized floating-point and rounding
exponent
1 bit 6 bit 14 bit
mantissa
0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
copy to register in processor
1 .
leading one two extrarounding digits
0 00 1 0 1 0 1 0 1 0 1 0 1 0 11 1 1 1 1 1+
Numerical exceptions
zero (lowest exponent)
+ infinite (highest exponent)
- infinite
0 / 0
0 * infinite
infinite - infinite
Specialcoding for :
The machinestops at :
The instruction set - Arithmetic
• Addition Ls1 01 100000• Subtraction Ls2 01 101000• Multiplication Lm 01 001000• Division Li 01 010000• Square root Lw 01 011000
mnemonic
8-bit code
The instruction set - data handling
• Load Pr 11---------• Store Ps 10---------
• Binary to decimal Ld 01 111000• Decimal to binary Lu 01 110000
mnemonic
8-bit code
A simple program (a+b)*c
Lu read decimal number to Register 1Lu read decimal number to Register 2Ls1 add Ps 10 store result in address 10Lu read decimal number to Register 1Pr 10 read from address 10 to Register 2Lm multiply Ld show the decimal result
The microsequencers
conducting rod: advancesone position per cycle
step 1
step 2
step 3
step 4
step 5
Carry look-ahead
•Addition was performed in three steps:• compute sum (XOR)• compute all propagated carries• produce final result
•With relays addition can be performed in constant time (not logarithmic time)
Shifting
•Shifting can be done using a shifting tree (in logarithmic time)
•With relays shifting can be done in constant time
Transform all operations
•Compute at the beginning of each section t :
t = 1 - [(b1 - z1)(b2 - z2)(b3 - z3)]2
•t is only zero if we are in the desired section
Transform operations
Transform
a = b op c
into
a = a t + (b op c) (1 - t)
this means: only operations in the desired sectionmodify the memory contents
The halting problem
•But how do we stop the
loop? -compute 0/q in
each iteration-the
machine stops when q=0
Summary
Z1 36-38
Z2 39
Z3 39-41
Z4 42-45
The logarithmicmachine
The „logical“machine
Theoretical machines Algebraic machines Special machines
S1 42S2 44
The S1 and S2 (1942-44): fixed point Z3‘s
Binary memory (5-6 words)
Numerickeyboard
Numericdisplay
control unit
punchedtape
mantissa
FP processor
exponent mantissa
processor (relays)
Program
Das Pipeline
•Dr. Frank Darius (FU Berlin) - Schaltungsentwurf•Georg Heyne (Fritz-Haber-Institut) -
Hardwareentwurf•Wolfram Däumel (Fritz-Haber-Institut) - Layout• Lothar Schönbein (Fritz-Haber-Institut) - Fertigung• Torsten Vetter (Fritz-Haber-Institut) -
Mikrokontroller• Cüneyt Göktekin (FU Berlin) Programmierung• Mit Beiträgen von: Alexander Thurm, Fabian Stehn, Georg
Wittenburg (FU Berlin)