ISRO CSE 2016 | Question: 12

Question

The logic circuit given below converts a binary code $Y_1Y_2Y_3$ into 

• A. Excess-$3$ code
• B. Gray code
• C. $\text{BCD}$ code
• D. Hamming code

Comments

answer is 100% 

1. Gray code because B1  = G1 , B2 = G1 exor G2 , B3 = G2 exor G3 , so y is Gray code

Answer 1

Y	X
000	000
001	001
010	011
011	010
100	111
101	110
110	100
111	101

$X$ is a GRAY code as for consecutive numbers the change in bit position is only 1. 

From Wikipedia,

More formally, a Gray code is a code assigning to each of a contiguous set of integers, or to each member of a circular list, a word of symbols such that each two adjacent code words differ by one symbol. These codes are also known as single-distance codes, reflecting the Hamming distance of 1 between adjacent codes. There can be more than one Gray code for a given word length, but the term was first applied to a particular binary code for the non-negative integers, the binary-reflected Gray code, or BRGC, the three-bit version of which is shown above.

So, the given code is not GRAY code as the codes for 3-4, as well as 7-0 differs by 2 bits and not 1. It is also neither BCD (same as binary for 3 bits) nor Excess-3. So, answer should be none of these. 

Comments

@vandana There can be more than one GRAY code for a given word length. But as rohini pointed out, this is not Gray code. I have corrected..

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Thank you sir.

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sir it simply a conversion from grey to binary na ? if they mention binary code then is it true ?

Answer 2

well when we have Gray code,and we convert from gray to binary code then this circuit will work perfectly taking any example u can ascertain the statement ,since no option says something like this ,question become wrong

Answer 3

Ans is c but in isro key answer is b.

 

Because for gray code no output take as a input but her it is given so it is not gray code

 In bcd code we take output as a input for next gate other then most significant bit

Comments

In question according to gray code representation y2 is connected to 2nd exor in place of x2

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In BCD , each digit is represented by its binary equivalent. So  BCD for 100 (4) should be 100. But circuit represents 111 for 100.

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M etna to nhi jaanta but for gray code In question y2 is connected to 2nd exor in place of x2

Answer 4

Y	X
110	100
000	000
001	001
111	101
100	111
010	011
011	010
101	110

X is gray Code.

Hence, Answer is B. Gray code

Comments

Then simply make a circuit which does nothing but takes the same output and input a GRAY code to it and say the circuit produces a GRAY code :)

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So, the answer is correct?

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No, the gray code should be produced for the input sequence 000, 001, 010 ...

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the given circuit is conversion of gray code to binary codes