logic gates. and function output y is true if inputs a and b are true, else it is false. logic...
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Logic GatesLogic Gates
AND FunctionOutput Y is TRUE if inputs A AND B are TRUE, else it is FALSE.
Logic Symbol
Text Description
Truth Table
Boolean Expression
ANDA
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 = A Y = 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 inverterThis 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
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 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
00
0
0
1 0
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 0 1 1 1
A B C Y0
OR
A
Y
NOT
AND
B
CAND
00
1
0
1 1
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 Y010
OR
A
Y
NOT
AND
B
CAND
01
0
0
1 0
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 0 1 1 1
A B C Y010
0
OR
A
Y
NOT
AND
B
CAND
01
1
0
1 1
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 Y0101
0
OR
A
Y
NOT
AND
B
CAND
10
0
0
0 0
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 0 1 1 1
A B C Y01010
0
OR
A
Y
NOT
AND
B
CAND
10
1
0
0 0
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 0 1 1 1
A B C Y010100
0
OR
A
Y
NOT
AND
B
CAND
11
0
1
0 0
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 Y0101001
0
OR
A
Y
NOT
AND
B
CAND
11
1
1
0 0
1
1
Circuit-to-Boolean Equation
OR
A
Y
NOT
ANDB
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
ANDB
CAND
AND Gates
INVERTER Gates
OR GatesOther Logic Arrangements:
NAND - NAND LogicNOR - NOR Logic
NAND Gate – Special Application
INPUTS OUTPUT
A B Y0 0 10 1 11 0 11 1 0
A
BYNAND
TNANDS
S T0010 11 0
Equivalent To An Inverter Gate
NOR Gate - Special Application
S T0010 11 0
Equivalent To An Inverter Gate
TS NOR
A
BYNOR
INPUTS OUTPUT
A B Y0 0 10 1 01 0 01 1 0