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Short Note on Gray Code and Excess-3 Code.

Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 7 M

Year: May 11

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## a) Gray Code:-

• Gray Code is non- weighted code and is a special case of unit-distance code.
• In unit-distance code, bit pattern for two consecutive number differ in only one bit position.

These codes are also called as cyclic code for Example;

Gray cod for decimal number 5 is 0 1 1 1 and

Gray cod for decimal number 6 is 0 1 0 1 .

These two codes only differs by one bit position.

• This code is extensively used in shaft encoder because of this property.

• Gray Code is reflected code.
• Gray code can be constructed using following property.

i) A 1 Bit Gray Code has two code words 0 and 1 representing Decimal No. 0 and 1 respectively.

ii) An (n-bit) n>2 Gary Code will have first 2n-1 Gray Codes of (n-1) bit written in order write leading 0 appended.

iii) The last 2n-1 Gray Code will be equal to Gray Code words of an (n-1) bit Gray Code, written in reverse order.

## b) Excess-3 Code

• This is another form BCD Code, on which each Decimal Digit is coded into 4-bit Binary code.
• The code for each Decimal Digit obtained by adding 3 to natural BCD code of the digit. • It is not-weighted code
• This code is self – complementing code, which means 1’s complement of the coded number yields 9’s complement of number itself

For Example,

Excess-3 Code for 2 is 0 1 0 1 and it’s 1’s complement is 1 0 1 0 which is Excess-3 code for decimal 7, which is 9’s complement of 2

• The self – complementing property of this code used in performing subtracting operation in digital system.
• Excess-3 code for decimal 0 through 9 given below :
Decimal Digit Excess-3 Code
0 0 0 1 1
1 0 1 0 0
2 0 1 0 1
3 0 1 1 0
4 0 1 1 1
5 1 0 0 0
6 1 0 0 1
7 1 0 1 0
8 1 0 1 1
9 1 1 0 0