2018 A/L Physics Past Paper · Question 10 (English Medium)

Gate equivalent to the logic circuit

The logic circuit shown in figure (a) is equivalent to

(1) Figure (1) — AND
(2) Figure (2) — OR
(3) Figure (3) — NAND
(4) Figure (4) — XOR
(5) Figure (5) — XNOR

Answer and explanation

Answer: (5) Figure (5) — XNOR

What the question asks

The inputs are $A$ and $B$ .

The top AND gate gets $A$ and $B$ . The bottom AND gate gets $\bar{A}$ and $\bar{B}$ through the NOT gates.

Both outputs go into the OR gate.

The logic expression for the XNOR gate can be given as "When only one of the inputs A or B is 1, the output is 0"

This gives 1 only when the inputs are equal.

$AB$

$\bar{A}\,\bar{B}$

$F = AB + \bar{A}\,\bar{B}$

The F column is $1, 0, 0, 1$ . $F = 1$ when the inputs are equal.

A = 0, B = 0

F = 1

$\bar{A}\bar{B} = 1$ . The bottom AND gives 1. So the OR gives 1.

A = 0, B = 1

F = 0

$AB = 0$ and $\bar{A}\bar{B} = 0$ . Both AND gates give 0.

A = 1, B = 0

A = 1, B = 1

$AB = 1$ . The top AND gives 1. So the OR gives 1.

AND gives $0, 0, 0, 1$ . It is wrong in the row $A = B = 0$ .

OR gives $0, 1, 1, 1$ . It is wrong in three rows.

NAND gives $1, 1, 1, 0$ . It is wrong in the rows with $A \neq B$ and in the last row.

XOR gives $0, 1, 1, 0$ . It is the opposite in every row.

$F = AB + \bar{A}\bar{B} = \overline{A \oplus B}$

$F = AB + \bar{A}\bar{B}$

The table is $1, 0, 0, 1$ . That is the XNOR gate.

The answer is option (5).

Think of XNOR as the "same gate".

When the inputs are the same, the output is 1.

Exam tip