To convert a Gray code into an ordinary binary number, the most significant bit is used as it is, and each lower bit is found as the exclusive OR of the binary bit already found one position higher and the Gray code bit in the same position. Which of the following is the 4-bit Gray code 1101 converted into binary?

Answer: A. 1001 (decimal 9)

The most significant bit is 1, the next is 1 ⊕ 1 = 0, the next 0 ⊕ 0 = 0 and the least significant 0 ⊕ 1 = 1, so the binary number is 1001 (decimal 9). As a check, the exclusive OR of 1001 and 0100, which is 1001 shifted right by 1 bit, is 1101, the original Gray code. In the Gray code, adjacent values differ in only one bit, as in 8 = 1100, 9 = 1101 and 10 = 1111.

• A. Correct. Finding 1, 1 ⊕ 1, 0 ⊕ 0 and 0 ⊕ 1 in turn gives 1001.
• B. 1011 is the result of applying the binary-to-Gray conversion (exclusive OR of adjacent bits) to 1101; the conversion goes the wrong way.
• C. 1101 is the value of the Gray code read as it is as a binary number.