GATE | GATE-CS-2006 | Question 40

Consider numbers represented in 4-bit gray code. Let h3h2h1h0 be the gray code representation of a number n and let g3g2g1g0 be the gray code of (n + 1) (modulo 16) value of the number. Which one of the following functions is correct?

A: g_{0}(h_{3},h_{2},h_{1},h_{0})=\sum (1,2,3,6,10,13,14,15)
B: g_{1}(h_{3},h_{2},h_{1},h_{0})=\sum (4,9,10,11,12,13,14,15)
C: g_{2}(h_{3},h_{2},h_{1},h_{0})=\sum (2,4,5,6,7,12,13,15)
D: g_{3}(h_{3},h_{2},h_{1},h_{0})=\sum (0,1,6,7,10,11,12,13)
(A) A
(B) B
(C) C
(D) D


Answer: (C)

Explanation: Write gray code (n) numbers from 0 to 15 and make another column for (n+1) numbers by shifting the next number on top. As shown in the table:

gray-code

Now to determine the min terms for g3, g2, g1, g0, we see the ‘1s’ in the corresponding columns. The digit they correspond to give the min terms of the function. Thus the answers we will be:

G3(h3h2h1h0)= ∑(4,12,13,15,14,10,11,9)
G2(h3h2h1h0)= ∑(2,6,7,5,4,12,13,15)
G1(h3h2h1h0)= ∑(1,3,2,6,13,15,14,10)
G0(h3h2h1h0)= ∑(0,1,6,7,12,13,10,11)

Thus g2 is given correctly in the options.

Read about K-Maps to know about mapping, SOP and POS forms:

K-Map (Karnaugh Map)

Watch NPTEL videos to learn more about:

Code converters
Logic Minimization Using Karnaugh Maps
Karnaugh Map Minimization Using Maxterms

This explanation has been contributed by Kriti Kushwaha.


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