Digital-Logic-Design

Question 14

Consider the circuit given below which has a four bit binary number b₃b₂b₁b₀ as input and a five bit binary number d₄d₃d₂d₁d₀ as output. The circuit implements:

A	Binary of Hex conversion
B	Binary to BCD conversion
C	Binary to grey code conversion
D	Binary to radix-12 conversion

Digital-Logic-DesignAdderGATE 1996

Question 14 Explanation:

Here ф means 0.
Whenever, b₂ = b₃ = 1, then only 0100, i.e., 4 is added to the given binary number. Lets write all possibilities for b.

Note that the last 4 combinations leads to b₃ and b₂ as 1. So, in these combinations only 0010 will be added.
1100 is 12
1101 is 13
1110 is 14
1111 is 15
in binary unsigned number system.
1100 + 0100 = 10000
1101 + 0100 = 10001, and so on.
This is conversion to radix 12.

Correct Answer: D

Question 14 Explanation:

Here ф means 0.
Whenever, b₂ = b₃ = 1, then only 0100, i.e., 4 is added to the given binary number. Lets write all possibilities for b.