State truth table of 3 bit Gray to Binary conversion then design it using 3:8 decoder and additional gates.

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written 3.6 years ago by

teamques10 ★ 68k

Truth table:

Decimal	Gray Code input	Binary output
	G2	G1	G0	B2	B1	B0
0	0	0	0	0	0	0
1	0	0	1	0	0	1
2	0	1	1	0	1	0
3	0	1	0	0	1	1
4	1	1	0	1	0	0
5	1	1	1	1	0	1
6	1	0	1	1	1	0
7	1	0	0	1	1	1

Output expression

$B_2=0_4+0_5+0_6+0_7 \\[2ex] B_1=0_3+0_4+0_6+0_7 \\[2ex] B_0=0_1+0_3+0_5+0_7$

Implementation using 3:8 decodex

For active low outputs, modified expression are :-

$B_2=\overline{\overline{(0_4+0_5+0_6+0_7 )}}=\overline{ \overline{0_4.0_5.0_6 .0_7 }} \\[2ex] B_1=\overline{\overline{(0_3+0_4+0_6+0_7 )}}=\overline{ \overline{0_3.0_4.0_6 .0_7 }} \\[2ex] B_0=\overline{\overline{(0_1+0_3+0_5+0_7 )}}=\overline{ \overline{0_1.0_3.0_5 .0_7 }} $

ADD COMMENT EDIT

Decimal	Gray Code input	Binary output
	G2	G1	G0	B2	B1	B0
0	0	0	0	0	0	0
1	0	0	1	0	0	1
2	0	1	1	0	1	0
3	0	1	0	0	1	1
4	1	1	0	1	0	0
5	1	1	1	1	0	1
6	1	0	1	1	1	0
7	1	0	0	1	1	1

Decimal	Gray Code input	Binary output
	G2	G1	G0	B2	B1	B0
0	0	0	0	0	0	0
1	0	0	1	0	0	1
2	0	1	1	0	1	0
3	0	1	0	0	1	1
4	1	1	0	1	0	0
5	1	1	1	1	0	1
6	1	0	1	1	1	0
7	1	0	0	1	1	1

Decimal	Gray Code input	Binary output
	G2	G1	G0	B2	B1	B0
0	0	0	0	0	0	0
1	0	0	1	0	0	1
2	0	1	1	0	1	0
3	0	1	0	0	1	1
4	1	1	0	1	0	0
5	1	1	1	1	0	1
6	1	0	1	1	1	0
7	1	0	0	1	1	1