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.

  For Example,2 is loaded as

• 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 :