57. Gray to Binary Code Converter

A 4-bit Gray-to-Binary converter uses a cumulative XOR structure.

The most significant Binary output is identical to the most significant Gray input:

D3 = G3

Each remaining Binary output is generated by XORing the previous Binary output with the next Gray input:

D2 = D3 ⊕ G2
D1 = D2 ⊕ G1
D0 = D1 ⊕ G0

Substituting the previous results gives:

D3 = G3
D2 = G3 ⊕ G2
D1 = G3 ⊕ G2 ⊕ G1
D0 = G3 ⊕ G2 ⊕ G1 ⊕ G0

The circuit therefore requires three cascaded XOR gates and one direct connection.