What is the defining property of Gray code?

Successive numbers differ in exactly one bit

Each bit has weights 8, 4, 2, 1

Each decimal digit is coded as digit + 3

Successive numbers differ in exactly two bits

How does Gray code differ from binary in weighting?

Gray is unweighted; binary is weighted

Gray is weighted; binary is not

Why is Gray code not used for arithmetic?

It is unweighted, so arithmetic is not suitable

2079 Bhadra · 2+2+2 marks

Gray vs binary code, convert (10110)₂ to Gray

Short answer

Gray code is unweighted; consecutive numbers differ in exactly one bit, unlike weighted binary where many bits can change. To convert (10110)₂ to Gray: keep MSB 1, then G₃=1⊕0=1, G₂=0⊕1=1, G₁=1⊕1=0, G₀=1⊕0=1 → (11101)Gray.

What is a Gray code? How is it different than binary code? Convert (10110)₂ to Gray code?

Gray code

Gray code is an unweighted binary code in which two successive values differ in only one bit. It is also called the reflected binary code. Example sequence: 000, 001, 011, 010, 110, 111, 101, 100.

Difference from binary code

Point	Binary code	Gray code
Weights	Weighted (1, 2, 4, 8…)	Unweighted
Bit change between successive numbers	One or more (011 → 100 changes 3 bits)	Exactly one
Arithmetic	Easy	Not suitable
Switching errors	Possible at transitions	Minimal
Uses	Computation, storage	Encoders, K-maps, ADCs

Convert $(10110)_2$ to Gray

Keep the MSB; each following Gray bit is the XOR of two adjacent binary bits.

 Binary: 1   0   1   1   0
         | \ | \ | \ | \ |
 Gray  : 1   1   1   0   1

$G_4 = B_4 = 1$
$G_3 = 1 \oplus 0 = 1$
$G_2 = 0 \oplus 1 = 1$
$G_1 = 1 \oplus 1 = 0$
$G_0 = 1 \oplus 0 = 1$

Answer: $(10110)_2 = (11101)_{Gray}$

✓ Answer checked by Claude Opus 5.5 (high effort)

Gray code, (11101)Gray to binary, FFH AND CAH · Digital Logic, chapter 1
BCD code and 3-bit binary-to-Gray converter · Digital Logic, chapter 1
Gray code and 3-bit binary-to-Gray converter · Digital Logic, chapter 1
Gray code compared with binary numbers · Digital Logic, chapter 1
Convert (110111)gray to binary · Digital Logic, chapter 1
Convert (01010111)gray to binary · Digital Logic, chapter 1
5-bit R-2R DAC output for 10110 · Advanced Electronics, chapter 3
Convolutional vs block codes; (7,4) cyclic code for 1011 · Communication Systems, chapter 8 · asked 2×
Convolutional vs block coder; (7,4) cyclic code for 1010 · Communication Systems, chapter 8 · asked 2×

All Digital Logic chapter 1 questions →

Gray vs binary code, convert (10110)₂ to Gray

Gray code

Difference from binary code

Convert (10110)2(10110)_2(10110)2​ to Gray

Related questions

Convert $(10110)_2$ to Gray