## Binary To Gray Code And Gray To Binary Code

AIM: To realize 4-Bit Code Converter: Realization using XOR gates.

### Binary to Gray:

The 4 bit combination assigned to Binary Code to Gray. four bits to represent a decimal digit. There are four inputs and four outputs. The input variable are defined as B3, B2, B1, B0 and the output variables are defined as G3, G2, G1, G0. from the truth table, combinational circuit is designed.

B3 = G3

B2 ⊕ B3 = G2

B1 ⊕ B2 = G1

B0 ⊕ B1 = G0

BINARY TO GRAY OUTPUT TRUTH TABLE

 Sno. Binary Code Gray Code 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 0 0 1 0 1 7 0 1 1 1 0 1 0 0 8 1 0 0 0 0 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

### Gray to Binary:

The 4 bit combination assigned to Gray to Binary Code. four bits to represent a decimal digit. There are four inputs and four outputs. The input variable are defined as G3, G2, G1, G0 and the output variables are defined as B3, B2, B1, B0. from the truth table, combinational circuit is designed.

G0 ⊕ G1 ⊕ G2 ⊕ G3 = B0

G1 ⊕ G2 ⊕ G3 = B1

G2 ⊕ G3 = B2

G3 = B3

GRAY TO BINARY OUTPUT TRUTH TABLE

 Sno. Gray Code Binary Code G3 G2 G1 G0 B3 B2 B1 B0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 2 0 0 1 1 0 0 1 0 3 0 0 1 0 0 0 1 1 4 0 1 1 0 0 1 0 0 5 0 1 1 1 0 1 0 1 6 0 1 0 1 0 1 1 0 7 0 1 0 0 0 1 1 1 8 0 1 0 0 1 0 0 0 9 1 1 0 1 1 0 0 1 10 1 1 1 1 1 0 1 0 11 1 1 1 0 1 0 1 1 12 1 0 1 0 1 1 0 0 13 1 0 1 1 1 1 0 1 14 1 0 0 1 1 1 1 0 15 1 0 0 0 1 1 1 1
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Binary To Gray Code & Gray To Binary Code

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#### Arvind Ahir

Im Arvind Ahir Student Study Btech CSE , Skills Web Developer,Networking ,Arduino .