Gray Code → Binary Converter

Enter a 4-bit Gray code. Three cascaded XOR gates decode it back to binary. Each output feeds the next gate — the cascade propagates MSB to LSB.

Gray → Binary Circuit (4-bit, cascaded XOR)

0G3 0G2 0G1 0G0 XOR XOR XOR B30 B20 B10 B00 GRAY BINARY
Gray 0000
Binary 0000 = 0

Truth Table (all 16 codes)

G3G2G1G0B3B2B1B0Dec
0000 0000 0
0001 0001 1
0010 0011 3
0011 0010 2
0100 0111 7
0101 0110 6
0110 0100 4
0111 0101 5
1000 1111 15
1001 1110 14
1010 1100 12
1011 1101 13
1100 1000 8
1101 1001 9
1110 1011 11
1111 1010 10

Cascaded XOR Explained

Formula

B3 = G3
B2 = B3 ⊕ G2
B1 = B2 ⊕ G1
B0 = B1 ⊕ G0

Why Cascaded?

Each XOR gate's output feeds directly into the next gate's input — this serial propagation is the key difference from the parallel B→G direction.

Inverse Operation

G→B is the exact inverse of B→G. Try 1011 Gray here — you should get the same Binary you entered in B→G lab when output was 1011.