The Excess-3 code of decimal 3 is:

Excess-3 Code (XS-3 Code)

Definition

Excess-3 code is a non-weighted Binary Coded Decimal (BCD) code obtained by adding 3 to each decimal digit and then converting it into binary.

Excess-3 code is a 4-bit non-weighted, self-complementing, biased sequential code obtained by adding 3 to each decimal digit before binary conversion.

It is called Excess-3 because:
Excess-3 = {Decimal Number} + 3

Or

XS-3 = BCD + 0011

Steps to Convert Decimal to Excess-3

1. Take the decimal digit.

2. Add 3 to it.

3. Convert the result into 4-bit binary.

Excess-3 Code Table

Example 1

Convert Decimal 3 into Excess-3

Step 1:
3 + 3 = 6

Step 2:

Binary of 6: 0110

Answer: 3 ----> 0110

Example 2

Convert Decimal 27 into Excess-3

Convert each digit separately.

For 2:
2+3=5 ---> 0101

For 7:
7+3=10 ----> 1010

Answer:
27 ----->0101 1010

Important Points About Excess-3 Code

1. Non-Weighted Code

It does not have fixed positional weights like:

• 8421 BCD

So it is called a non-weighted code.

2. Self-Complementing Code

Excess-3 is a self-complementing code.

Meaning:

• Taking the 1’s complement of a code gives the Excess-3 code of the 9’s complement digit.

If:
XS-3 of N =X

then: 1's complement of X gives : XS-3 of (9- N)

Example:

Excess-3 of 2:
0101

1’s complement:
1010
1010 = 7

And:
9 - 2 = 7

3. No Representation for Invalid Decimal Digits

Only decimal digits 0–9 are represented.

4. Sequential Code

Excess-3 is also called a sequential code because code values increase sequentially as decimal digits increase.

Example:

The binary sequence increases in order.

Excess-3 is a 4-bit non-weighted self-complementing sequential code.
Valid XS-3 codes range from 0011 to 1100, while the remaining combinations are invalid (0000,0001,0010,1101,1110,1111).

Conversion of Excess-3 (XS-3) to Binary

To convert Excess-3 code to binary/decimal, follow these steps:

Method

Step 1:

Divide the XS-3 code into 4-bit groups.

Step 2:

Convert each 4-bit group into decimal.

Step 3:

Subtract 3 from each decimal value.

Step 4:

Write the final decimal/binary number.

To convert Excess-3 (XS-3) code into decimal:

Rule

Decimal Digit = Binary Value - 3

1. XS-3 Code = 1000

Binary to Decimal
10002 = 8

Subtract 3
8 - 3 = 5

Answer: 5

2. XS-3 Code = 1010

Binary to Decimal
10102 = 10

Subtract 3
10 - 3 = 7

Answer: 7

3. XS-3 Code = 0110

Binary to Decimal
01102 = 6

Subtract 3
6 - 3 = 3

Answer: 3

4. XS-3 Code = 0001

Binary to Decimal
00012 = 1

Subtract 3
1 - 3 = -2

But: 0001 is NOT a valid Excess-3 code.

Valid XS-3 codes range from:
0011 to 1100

✅ Final Answers