Question

Explain the Derived gates with expression and truth table.

Answer 1

The logic gates like NAND, NOR, XOR, and XNOR are derived gates that are derived from the fundamental gates AND, OR, NOT.

(i) NAND gate:

The NAND is the combination of NOT and AND. The NAND is generated by inverting the output of an AND operation.

Output: Y = `overline"AB"`

Logic circuit

Logic symbol:

Truth table:

Inputs		Output
A	B	y = `overline"A . B"`
0	0	1
0	1	1
1	0	1
1	1	0

Inputs Outputs

(ii) NOR gate:

The NOR is the combination of NOT and OR. The NOR is generated by inverting the output of an OR operation.

Logic function: y = `overline"A + B"`

Logic circuit:

logic symbol:

Inputs		Output
A	B	y = `overline"A + B"`
0	0	1
0	1	0
1	0	0
1	1	0

(iii) XOR gate:

The XOR (exclusive – OR) gate acts in the same way as the logical either /or.

Logic symbol:

Logic circuit:

Truth table:

Inputs		Outputs
A	B	C
0	0	0
0	1	1
1	0	1
1	1	0

(iv) XNOR gate:

XNOR gate (exclusive – NOR) gate is a combination of XOR gate followed by an inverter.

Logic function: y = `overline"AB"`

logic symbol:

Inputs		Outputs
A	B	C
0	0	1
0	1	0
1	0	0
1	1	1

Boolean function:

C = `overline("A" ⊕ "B")`

= `overline"A" * "B" + "A" * overline"B"`

= AB + `bar"A" * bar"B"`