Question

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?
1. g₀ (h₃ h₂ h₁ h₀) = Σ(1,2,3,6,10,13,14,15)
2. g₁ (h3 h2 h1 h0)
3. g₂ (h3 h2 h1 h0)
4. g₃ (h3 h2 h1 h0)

Answer 1

"Correct Answer - Option 3 : g₂ (h3 h2 h1 h

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)

"