# 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:

1. Convert the binary number into decimal.
2. Add 3 in each digit of the decimal number.
3. 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.

Operation Quotient Remainder
30/2 15 0 (LSB)
15/2 7 1
7/2 3 1
3/2 1 1
1/2 0 1(MSB)

(30)10=(11110)2

So, the binary number of excess-3 code 01100011 is: (11110)2

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