NIMCET 2015 Question Paper with solutions

Question : 119 of 120

Marks: +1, -0

Consider 4-bit gray code representation of numbers.Let

h_3h_2h_1h_0

be the gray code representation of anumber ‘n’ and

g_3g_2g_1g_0

be the gray coderepresentation of the number (n+1) modulo 16. Whichone of the following functions is correct.

Solution:

Binary	h	$h_3\;h_2\;h_1\;h_0$	(n+1)mod 16	$g_3\;g_2\;g_1\;g_0$
0000	0	0000	1	0001
0001	1	0001	2	0011
0010	2	0011	3	0010
0011	3	0010	4	0110
0100	4	0110	5	0111
0101	5	0111	6	0101
0110	6	0101	7	0100
0111	7	0100	8	1100
1000	8	1100	9	1101
1001	9	1101	10	1111
1010	10	1111	11	1110
1011	11	1110	12	1010
1100	12	1010	13	1011
1101	13	1011	14	1001
1110	14	1001	15	1000
1111	15	1000	0	0000

This gives the solution option (b).

g_1(h_3\;\;h_2\;\;h_1\;\;h_0)=Σ(4,9,10,11,12,13,14,15)

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