2.2 boolean algebra
TRANSCRIPT
2.2Perform operations
with Boolean AlgebraLOGIC GATES, TRUTH TABLE, AND IT’S
OPERATIONS
What is Logic Gates?
Logic gates in binary system is
use to represent process and
operation for binary
information in matematic.
AND FunctionOutput Y is TRUE if inputs A AND B are
TRUE, else it is FALSE.
Logic Symbol
Text Description
Truth Table
Boolean Expression
AND
A
BY
INPUTS OUTPUT
A B Y
0 0 0
0 1 0
1 0 0
1 1 1 AND Gate Truth Table
Y = A x B = A • B = AB
AND Symbol
OR FunctionOutput Y is TRUE if input A OR B is
TRUE, else it is FALSE.
Logic Symbol
Text Description
Truth Table
Boolean Expression Y = A + B
OR Symbol
A
BYOR
INPUTS OUTPUT
A B Y
0 0 0
0 1 1
1 0 1
1 1 1 OR Gate Truth Table
NOT Function (inverter)
Output Y is TRUE if input A is FALSE,
else it is FALSE. Y is the inverse of
A.
Logic Symbol
Text Description
Truth Table
Boolean Expression
INPUT OUTPUT
A Y
0 1
1 0 NOT Gate Truth Table
A YNOT
NOT
Bar
Y = AY = A’
Alternative Notation
Y = !A
NAND FunctionOutput Y is FALSE if inputs A AND B
are TRUE, else it is TRUE.
Logic Symbol
Text Description
Truth Table
Boolean Expression
A
BYNAND
A bubble is an inverter
This is an AND Gate with an inverted output
Y = A x B = AB
INPUTS OUTPUT
A B Y
0 0 1
0 1 1
1 0 1
1 1 0 NAND Gate Truth Table
NOR FunctionOutput Y is FALSE if input A OR B is
TRUE, else it is TRUE.
Logic Symbol
Text Description
Truth Table
Boolean Expression Y = A + B
A
BYNOR
A bubble is an inverter.
This is an OR Gate with its output inverted.
INPUTS OUTPUT
A B Y
0 0 1
0 1 0
1 0 0
1 1 0 NOR Gate Truth Table
Ex-OROutput C is FALSE if inputs A and B are same value,
else output is TRUE.
Symbol:
A
C
B
Get Exclusive (EX-OR)
Truth Table
Boolean Expression
INPUTS OUTPUT
A B C
0 0 0
0 1 1
1 0 1
1 1 0 EX-OR Gate Truth Table
Ex-NOROutput C is TRUE if inputs A and B are same value, else
output is FALSE.
Symbol:
AC
B
Get Exclusive (EX-NOR)
Truth Table
Boolean Expression
INPUTS OUTPUT
A B C
0 0 1
0 1 0
1 0 0
1 1 1 EX-NOR Gate Truth Table
Circuit-to-Truth Table Example
OR
A
Y
NOT
AND
B
CAND
2# of Inputs = # of Combinations
2 3 = 8
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
A B C Y
Circuit-to-Truth Table Example
OR
A
Y
NOT
AND
B
CAND
0 0 00 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
A B C Y
0
0
0
0
10
0
0
Circuit-to-Truth Table Example
0 0 0 0 0 10 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
A B C Y
0
OR
A
Y
NOT
AND
B
CAND
0
0
1
0
11
1
1
Circuit-to-Truth Table Example
0 0 0 0 0 1 0 1 00 1 1 1 0 0 1 0 1 1 1 0 1 1 1
A B C Y
010
OR
A
Y
NOT
AND
B
CAND
0
1
0
0
10
0
0
Circuit-to-Truth Table Example
0 0 0 0 0 1 0 1 0 0 1 11 0 0 1 0 1 1 1 0 1 1 1
A B C Y
010
0
OR
A
Y
NOT
AND
B
CAND
0
1
1
0
11
1
1
Circuit-to-Truth Table Example
0 0 0 0 0 1 0 1 0 0 1 1 1 0 01 0 1 1 1 0 1 1 1
A B C Y
0101
0
OR
A
Y
NOT
AND
B
CAND
1
0
0
0
00
0
0
Circuit-to-Truth Table Example
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 11 1 0 1 1 1
A B C Y
01010
0
OR
A
Y
NOT
AND
B
CAND
1
0
1
0
00
0
0
Circuit-to-Truth Table Example
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 01 1 1
A B C Y
010100
0
OR
A
Y
NOT
AND
B
CAND
1
1
0
1
00
1
1
Circuit-to-Truth Table Example
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
A B C Y
0101001
0
OR
A
Y
NOT
AND
B
CAND
1
1
1
1
00
1
1
Circuit-to-Boolean Equation
OR
A
Y
NOT
AND
B
CAND
A B
A C
A= A B + A C
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
A B C Y
0
0
00
0
11
}
1
1
}
A - O - I Logic
OR
A
Y
NOT
AND
B
CAND
AND Gates
INVERTER Gates
OR GatesOther Logic Arrangements:
NAND - NAND Logic
NOR - NOR Logic
NAND Gate – Special Application
INPUTS OUTPUT
A B Y
0 0 1
0 1 1
1 0 1
1 1 0
A
BYNAND
TNANDS
S T
0010 11 0
Equivalent To An Inverter Gate
NOR Gate - Special Application
S T
0010 11 0
Equivalent To An Inverter Gate
TS NOR
A
BYNOR
INPUTS OUTPUT
A B Y
0 0 1
0 1 0
1 0 0
1 1 0