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The Excess-$3$ code is also called

1. Cyclic Redundancy Code
2. Weighted Code
3. Self-Complementing Code
4. Algebraic Code

edited | 5.2k views

The Excess-3(XS3) code for a given decimal number is determined by adding '3' to each decimal digit in the given number and then replacing each digit of the newly found decimal number by its four bit binary equivalent. The table gives is the Excess-3 code. For example, XS3 code of 24 is obtained as

2       4

+3    +3

5       7

0101 0111

Thus, XS3 code of 24 is 0101 0111.

The key feature of the Excess-3 code is .that it is self complementing. In other words, the 1's complement of an Excess- 3 number is the Excess- 3 code for the 9's complement of the corresponding decimal number.

For example, the Excess- 3 code for decimal 6 is 1001. The 1's complement of 1001 is 0110, which is the Excess-3 code for decimal 3, and 3 is the 9's complement of 6. This property of Excess-3 code makes it useful in some arithmetic operations.

Hence,Option(C)Self-complimenting Code is the correct choice.

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The proof of this statement :

The 1's complement of an Excess- 3 number is the Excess- 3 code for the 9's complement of the corresponding decimal number.

Let's $x$ is the number that we are considering here ($0 \leq x \leq 9$ for Excess-3  rest are Pseudo-tetrade

Assuming $x$ is representated in decimal

Then the above statement can be written as :

$1's\ Complement(Excess3(x))=Excess3(9's\ Complement(x))$

Since $x$ is in decimal, $Excess3(x)=x+3$

$9's\ Complement(x)=9-x$

and $1's\ Complement(x)=15-x$ [Since $0 \leq x \leq 9$ so it is representated using 4 bits hence for finding $1's\ Complement$ we need to substract binary x from binary 1111 .i.e 15 - x  in decimal )

Now we can write the

$L.H.S = 1's\ Complement(Excess3(x))$

$\Rightarrow 1's\ Complement(x+3)$

$\Rightarrow 15-(x+3)$

$\Rightarrow 12-x$

$R.H.S=Excess3(9's\ Complement(x))$

$\Rightarrow Excess3(9-x)$

$\Rightarrow (9-x)+3$

$\Rightarrow 12-x$

Hence $L.H.S=R.H.S$

Excess 3 is Self-Complimenting code. It is also a Non-weighted Code

edited
Excess-3 code = BCD(1248) + 0011

After this we see that BCD(1248) is not Self Complementing code BUT Excess-3 code is Self Complementing code as well as Sequential code also.

Hence ans is (C) Self-Complementing Code
Self complement code

Excess-3 Code is also called

• XS-3 code
• Self-complimenting code

Option C

It is also non-weighted code, ie, the bit position doesn't play a role in determining the value. Other non-weighted codes: Gray Code.

Gray code is also called Reflected binary code, and it's considered a minimum error code.