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Binary Number for Gray Code 1011 is

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The binary number for Gray code 1011 is

A. 1011 
B. 1110 
C. 1101 
D. 0010 

Choose the right answer to the question from the options given above and also provide a detailed solution. 

Answer: C. 1101

The binary number for Gray code 1011 is 1101.

Solution:

Let G4G3G2G1G0 be the 4-bit Gray code and b4b3b2b1b0 be the corresponding binary code. We can find the binary code by using the following formulae.

b3=G3

b2=b3G2

b1=b2G1

b0=b1G0

Given, G4G3G2G1G= 1011.

b3=1

b2=1⊕0=1

b1=1⊕1=0

b0=0⊕1=1

=> b4b3b2b1b0=1101

Therefore, 1101 will be the corresponding binary code for the given Gray code 1011. Hence, Option (C) is the correct answer.

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