Basic logic gates

AND gate:The truth table is given byA.B B A

0 0 0

0 1 0

0 0 1

1 1 1

Logic circuit

LogicalOperator

Display

B

1

A

1

OR Gate logic circuit

LogicalOperator

Display

B

1

A

1

Truth table of OR Gate

Output B A0 0 01 1 01 0 11 1 1

NOT Gate(Invertor)

NOT _Gate A'A

1

NAND Gate

Output 'NAND

B

1

A

1

The Truth table of NAND Gate

Output B A1 0 01 1 01 0 10 1 1

NOR Gate Logic circuit

Output 'NOR

B

1

A

1

The truth table of NOR_gate

(A+B’) B A

1 0 0

0 1 0

0 0 1

0 1 1

XOR Gate (Exclusive-OR)

XOR Output '

B

0

A

1

The truth table of Exclusive-XOR Gate

Output B A0 0 01 1 01 0 10 1 1

XNOR Gate logic circuit

XOR Output '

1

NOT

B

0

A

0

The truth table of XNOR Gate

Oautput B A1 0 00 1 00 0 11 1 1

Basic combinational logic circuits

The SOP expressions are implemented with AND gate for each product term.

The OR Gate for summing all the product

terms.The SOP is called AND_OR logic

The AND-OR Logic (SOP)

SOPA.B+C.D

Output '

1

D

1C.D

C

0

B

1

A.BA

1

Exlusive OR Gate logic circuit

X=A.B'+A'.B Output '

1

NOT 1

NOT

B

1

A.B'

A'B

A

0

NAND gate as universal logic gate

Z'Z

1

Y'

Y".Z"=Y+Z

Y

1

X

0

OR_Gate

1

NOR_Gate

0

LogicalOperator 2

LogicalOperator 1

LogicalOperator

Inverter

0

D'D

1

C'

C".D"=C+D

C

1

B

1

AND_Gate

0

A

0

(Y+Z)'

The truth table for 4-input AND-OR circuit

Output CD AB D C B A0 0 0 0 0 0 00 0 0 1 0 0 00 0 0 0 1 0 01 1 0 1 1 0 00 0 0 0 0 1 00 0 0 1 0 1 00 0 0 0 1 1 01 1 0 1 1 1 00 0 0 0 0 0 10 0 0 1 0 0 10 0 0 0 1 0 11 1 0 1 1 0 11 0 1 0 0 1 1

NOR Gate as universal logic element

Z'Z

0 Y.Z

Y'Y

1

X

0

OR_Gate1

1

NOR_Gate 1

NOR1

NAND_Gate

1

Inverter

1

D'D

1

C'C

1

B

1

AND_Gate

1

A

0

(Y.Z)'

(A+B)'

(A '+B')'=A.B