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.
| 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