Convert 111001 to Gray code.

Convert 111001 to Gray code.

• A. 110001
• B. 100101
• C. 001100
• D. 010101

Answer: (B)

Converting binary to Gray code is done by XORing the number with itself shifted right by one bit. The leftmost bit stays the same, and each subsequent Gray bit is the XOR of two adjacent binary bits. For 111001, shift right by one to get 011100. Now XOR each bit: 1 XOR 0 = 1, 1 XOR 1 = 0, 1 XOR 1 = 0, 0 XOR 1 = 1, 0 XOR 0 = 0, 1 XOR 0 = 1. This gives 100101, which is the Gray code representation of 111001.

Converting binary to Gray code is done by XORing the number with itself shifted right by one bit. The leftmost bit stays the same, and each subsequent Gray bit is the XOR of two adjacent binary bits. For 111001, shift right by one to get 011100. Now XOR each bit: 1 XOR 0 = 1, 1 XOR 1 = 0, 1 XOR 1 = 0, 0 XOR 1 = 1, 0 XOR 0 = 0, 1 XOR 0 = 1. This gives 100101, which is the Gray code representation of 111001.