Excess-3 Code and its Conversion

Excess-3 code is a BCD code. It is a self-complementing code, but not a weighted code. In earlier articles, we have seen decimal to binary conversion, decimal to 8421 BCD conversion and vice versa. In this article, we will learn about Excess-3 code and its conversion.

Excess-3, as its name says, there is an excess of the number 3. That means we add 3 to a decimal digit to get the corresponding Excess-3 number. The following table shows the list of decimal digits, the corresponding 8421 BCD code and the Excess-3 code.

Decimal Digit	8421 BCD Code	Excess-3 BCD Code
0	0000	0011
1	0001	0100
2	0010	0101
3	0011	0110
4	0100	0111
5	0101	1000
6	0110	1001
7	0111	1010
8	1000	1011
9	1001	1100

Conversion of Excess-3 Code

We get the Excess-3 code of a corresponding decimal number by adding 3 to its individual digits.

Example: Find the Excess-3 code of (i) 1548, (ii) 23.9

Solution:

(i) To get the Excess-3 code, we will add 3 to each digit of the given decimal number. Since, the given number is 1548, a 4-digit number; we will add “3333” to the number.

1548 + 3333 = 0001_0101_0100_1000 + 0011_0011_0011_0011 = 0100_1000_0111_1011

Note: Notice that “3333” is replaced by its 8421 BCD equivalent, that is, “0011_0011_0011_0011”. ‘_’ added for better readability only.

(ii) To get the Excess-3 code, we will add 3 to each digit of the given decimal number, both for the digits before and after the decimal point. Since, the given number is 23.9, we will add “33.3” to the number.

23.9 + 33.3 = 0010_0011.1001 + 0011_0011.0011 = 0101_0110.1100

We get the decimal number from an Excess-3 code by subtracting 3 (0011) from its individual digit code.

Example: Find the decimal number of the Excess-3 code 1010_0110

Solution:

1010_0110 – 0011_0011 = 0111_0011 = 73

If we want to convert a binary number to an Excess-3 code or vice versa, then we need to take the decimal as the intermediary. This means for binary to Excess-3 code conversion; we need to convert the binary number to a decimal number first, then convert the decimal number to the final Excess-3 code as done above.

The following are a few advantages of Excess-3 code:

• Excess-3 code is beneficial for the arithmetic operation where the 8421 BCD addition exceeds the value 9.
• Excess-3 representation can be used as codeword representation for data transmitted on the transmission line as it does not use both 0000 and 1111, which are more prone to transmission error.
• Excess-3 code is self-complementing. Therefore, it is beneficial in the case of subtraction operation.

Previous           Table of Content           Next