Binary to Excess-3 code conversion

The excess-3 code plays an important role in representing the decimal numbers. The Excess-3 code can also be represented as the XS-3 code. In Excess-3 code, each digit of the decimal number is represented by adding 3 in each decimal digit. There are the following steps to convert the binary number into Excess-3 code:

Convert the binary number into decimal.
Add 3 in each digit of the decimal number.
Find the binary code of each digit of the newly generated decimal number.

We can also add 0011 in each 4-bit BCD code of the decimal number for getting excess-3 code.

Let's take an example to understand the process of converting a binary number into Excess-3 code.

Example 1: Convert (11110)₂ to Excess-3 using binary

1. First, convert the given binary number into a decimal number.

Binary Number: (11110)₂

Finding Decimal Equivalent of the number:

Steps	Binary Number	Decimal Number
1) Hb	(11110)₂	((1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰))₁₀
2)	(11110)₂	(16 + 8 + 4 + 2 + 0)₁₀
3)	(11110)₂	(30)₁₀

Decimal number of the Binary number (11110)₂ is (30)₁₀

2. Now, we add 3 in each digit of the decimal number.

The decimal number is 30. Now, we will add 3 into the decimal number 30.

= 30+33
= 63

3. Now, we find the binary code of each digit of the decimal number 63.

We write the binary code of each decimal digit in order to get Excess-3 code as:

Steps	Decimal Number	Conversion
Step 1	63₁₀	(0110)₂ (0011)₂
Step 2	63₁₀	(01100011)_Excess-3

Result:

(11110)₂ = (01100011)_Excess-3

Below is the table that contains the excess-3 code of the decimal and BCD.

Decimal Digit	BCD Code	Excess-3 Code
	A B C D	B₃B₂B₁B₀
0	0 0 0 0	0 0 1 1
1	0 0 0 1	0 1 0 0
2	0 0 1 0	0 1 0 1
3	0 0 1 1	0 1 1 0
4	0 1 0 0	0 1 1 1
5	0 1 0 1	1 0 0 0
6	0 1 1 0	1 0 0 1
7	0 1 1 1	1 0 1 0
8	1 0 0 0	1 0 1 1
9	1 0 0 1	1 1 0 0

In the above table, the most significant bit of the decimal number is represented by the bit B₃, and the least significant bits are represented by B₂, B₁, and B₀.

Excess-3 to Binary Conversion

The process of converting Excess-3 code into binary is opposite to the process of converting Binary code into Excess-3. There are the following steps to convert the Excess-3 code into binary:

In the first step, we will make the group of 4 bits and write the equivalent decimal number from the Excess-3 table.
At last, we find the binary number of the decimal number using a decimal to binary conversion.

Example 1: (01100011)_Excess-3

1) Making groups of four bits and write their equivalent decimal number.

(01100011)_Excess-3 = (0110 0011)_Excess-3

From the Excess-3 table:

(0110)_Excess-3 = (3)₁₀

(0011)_Excess-3 = (0)₁₀

So, the decimal number of excess-3 code 01100011 is: (30)₁₀

2) Find the binary number.

Now, find the binary number of the decimal number (30)₁₀ using a decimal to binary conversion as:

Divide the number 30 and its successive quotients with base 2.