In this circuit we’ll convert BINARY numbers to GRAY numbers. Following is the truth table for it:
B3 B2 B1 B0 G3 G2 G1 G0
0. 0 0 0 0 0 0 0 0
1. 0 0 0 1 0 0 0 1
2. 0 0 1 0 0 0 1 1
3. 0 0 1 1 0 0 1 0
4. 0 1 0 0 0 1 1 0
5. 0 1 0 1 0 1 1 1
6. 0 1 1 1 0 1 0 0
8. 1 0 0 0 1 1 0 0
9. 1 0 0 1 1 1 0 1
10. 1 0 1 0 1 1 1 1
11. 1 0 1 1 1 1 1 0
12. 1 1 0 0 1 0 1 0
13. 1 1 0 1 1 0 1 1
14. 1 1 1 0 1 0 0 1
15. 1 1 1 1 1 0 0 0
K-MAPS:
K-MAP FOR G3:
Equation for G3= B3
K-MAP FOR G2:
Equation for G2= B3’ B2 + B3 B2’= B3 XOR B2
K-MAP FOR G1:
Equation for G1= B1’ B2 + B1 B2’= B1 XOR B2
K-MAP FOR G0:
Equation for G0= B1’ B0 + B1 B0’= B1 XOR B0
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