The Gray-code equivalent of the binary number 1010 is:
2025
The Gray-code equivalent of the binary number 1010 is:
Answer: B. 1111 — Binary-to-Gray conversion rule: the most significant (leftmost) bit of the Gray code is identical to the most significant bit of the binary number. Each…
- A.
1100
- B.
1111
- C.
1010
- D.
0101
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Correct answer: B
Binary-to-Gray conversion rule: the most significant (leftmost) bit of the Gray code is identical to the most significant bit of the binary number. Each subsequent Gray-code bit is obtained by XOR-ing the corresponding binary bit with the binary bit immediately to its left (that is, g(i) = b(i) XOR b(i-1), with g(1) = b(1)).
Write the binary digits in order: b1 = 1, b2 = 0, b3 = 1, b4 = 0.
g1 = b1 = 1 (the leading bit is copied unchanged).
g2 = b1 XOR b2 = 1 XOR 0 = 1.
g3 = b2 XOR b3 = 0 XOR 1 = 1.
g4 = b3 XOR b4 = 1 XOR 0 = 1.
Concatenating g1 g2 g3 g4 gives the Gray code 1111.
Reconstruct the binary number back from 1111 using the inverse Gray-to-binary rule, b1 = g1 and b(i) = b(i-1) XOR g(i): b1 = 1, b2 = 1 XOR 1 = 0, b3 = 0 XOR 1 = 1, b4 = 1 XOR 1 = 0, giving back 1010 -- confirming the conversion.