56. Binary to Gray Code Converter

A 4-bit Binary-to-Gray converter uses the most significant Binary bit directly and XORs each pair of adjacent Binary bits to generate the remaining Gray-code outputs.

The output equations are:

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

G3 is connected directly to D3.

Three XOR gates generate the remaining outputs:

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

Therefore, the complete converter requires only three XOR gates and one direct connection.

All 0000–1111 Binary combinations are valid inputs, so the circuit does not require any don't-care conditions.