Binary to Excess-3 & Excess-3 to Binary Conversion | Digital Circuits - Electronics and Communication Engineering (ECE) PDF Download

Introduction


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:
Binary to Excess-3 & Excess-3 to Binary Conversion | Digital Circuits - Electronics and Communication Engineering (ECE)

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:
Binary to Excess-3 & Excess-3 to Binary Conversion | Digital Circuits - Electronics and Communication Engineering (ECE)Result:
(11110)2 = (01100011)Excess-3
Below is the table that contains the excess-3 code of the decimal and BCD.
Binary to Excess-3 & Excess-3 to Binary Conversion | Digital Circuits - Electronics and Communication Engineering (ECE)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.
Binary to Excess-3 & Excess-3 to Binary Conversion | Digital Circuits - Electronics and Communication Engineering (ECE)(30)10 = (11110)2
So, the binary number of excess-3 code 01100011 is: (11110)2

The document Binary to Excess-3 & Excess-3 to Binary Conversion | Digital Circuits - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Digital Circuits.
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