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Consider 4-bit gray code representation of numbers. Let  h3 h2 h1 h0 be the gray code representation of a number n and g1g2g3g0 be the gray code representation of the number (n + 1) modulo 16. Which one of the following functions is correct?

Consider 4-bit gray code representation of numbers. Let  h3 h2 h1 h0 be the gray code representation of a number n and g1g2g3g0 be the gray code representation of the number (n + 1) modulo 16. Which one of the following functions is correct? Correct Answer g<sub>2</sub> (h<span style="position: relative; line-height: 0; vertical-align: baseline; bottom: -0.25em; font-size:10.5px;">3</span> h<span style="position: relative; line-height: 0; vertical-align: baseline; bottom: -0.25em; font-size:10.5px;">2</span> h<span style="position: relative; line-height: 0; vertical-align: baseline; bottom: -0.25em; font-size:10.5px;">1</span> h<span style="position: relative; line-height: 0; vertical-align: baseline; bottom: -0.25em; font-size:10.5px;">0</span>) = Σ(2,4,5,6,7,12,13,15)

h3 h2 h1 h0 be the gray code representation of a number n and g1g2g3g0 be the gray code representation of the number (n + 1) modulo 16.

The truth table is as shown below.

Decimal

Binary

h3

h2

h1

h0

g3

g2

g1

g0

0

0000

0

0

0

0

0

0

0

1

1

0001

0

0

0

1

0

0

1

1

2

0010

0

0

1

1

0

0

1

0

3

0011

0

0

1

0

0

1

1

0

4

0100

0

1

1

0

0

1

1

1

5

0101

0

1

1

1

0

1

0

1

6

0110

0

1

0

1

0

1

0

0

7

0111

0

1

0

0

1

1

0

0

8

1000

1

1

0

0

1

1

0

1

9

1001

1

1

0

1

1

1

1

1

10

1010

1

1

1

1

1

1

1

0

11

1011

1

1

1

0

1

0

1

0

12

1100

1

0

1

0

1

0

1

1

13

1101

1

0

1

1

1

0

0

1

14

1110

1

0

0

1

1

0

0

0

15

1111

1

0

0

0

0

0

0

0

 

From the above truth table,

g3(h3 h2 h1 h0) = Σ(4, 9, 10, 11, 12, 13, 14, 15)

g2(h3 h2 h1 h0) = Σ(2, 4, 5, 6, 7, 12, 13, 15)

g1(h3 h2 h1 h0) = Σ(1, 2, 3, 6, 10, 13, 14, 15)

g0(h3 h2 h1 h0) = Σ(0, 1, 6, 7, 10, 11, 12, 13)

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