Digital Electronics Page

Gray Codes

This is a technique where we convert number from binary to grays. We do this because Gray reduces the bits we need to change to get to the next number. e.g. changing from 2 to 3 decimal requires a 1 bit change.

Decimal	BCD	Gray Code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111

Excess-3 Codes

To get an excess-3 code of a decimal number simply add 3 to each decimal digit. And then we write the 4-bit binary number for each digit of the decimal number. We can find the excess-3 code of the given binary number by using the following steps:

• We find the decimal number of the given binary number.
• Then we add 3 in each digit of the decimal number.
• Now, we 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.

Decimal	BCD	Excess-3
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

For example the excess-3 Code for 25.35 would be

25.35
33 33
-----
58 68

Which is

5 0100
8 1000
6 0110
8 1000

Therefore

01001000.01101000