UGC NET Computer Science December 2019 | Question 119

Question 119

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Which of the following binary codes for decimal digits are self complementing?
(a) 8421 code
(b) 2421 code
(c) excess-3 code
(d) excess-3 gray code

1. 1. (a) and (b)
2. 2. (b) and (c)
3. 3. (c) and (d)
4. 4. (d) and (a)

Answer : 2. (b) and (c)

Explanation Question 119

Self complementing codes are the codes that have the property that 9’s complement of a decimal number is obtained directly by replacing "1"s by "0"s and "0"s by "1"s i.e. by complementing each bit in the pattern.

Decimal Digit	2421 code	Excess 3-code	8421 code
0	0000	0011	0000
1	0001	0100	0001
2	0010	0101	0010
3	0011	0110	0011
4	0100	0111	0100
5	1011	1000	0101
6	1100	1001	0110
7	1101	1010	0111
8	1110	1011	1000
9	1111	1100	1001

Excess-3 code

• This code doesn’t have any weights. So, it is an un-weighted code.
• We will get the Excess 3 code of a decimal number by adding three 0011 to the binary equivalent of that decimal number. Hence, it is called as Excess 3 code.
• Excess-3 code is also called Self-Complementing Code. Because 1’s complement of excess-3 number is equivalent to 9’s complement of corresponding decimal digit.

2 4 2 1 code

• The weights of this code are 2, 4, 2 and 1.
• This code has all positive weights. So, it is a positively weighted code.
• It is an unnatural BCD code. Sum of weights of unnatural BCD codes is equal to 9.
• It is a self-complementing code. Self-complementing codes provide the 9’s complement of a decimal number, just by interchanging 1’s and 0’s in its equivalent 2421 representation.

Reference 1 : Excess-3 Code : Self-complementary property

Reference 2 : 2 4 2 1 code : a self-complementing code

So, option 2 is correct answer

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