When any number, letters, or word are represented by a special group of symbol or character we can say that they are being encoded and the group of symbol is called “CODE”
Various type of code are given
Non-Binary code: In non binary code system series of dots and dashes represents the letters of alphabet morse code is an example of non binary code
Binary code: In binary code system information is coded in group of binary digits examples are 8-4-2-1 code, BCD code , Excess-3 code , Gray code Error detecting and error correcting code
Alphanumeric code: In this code system information is coded in a set of elements that include the 10 decimal digits,the 26 letters of alphabet , and a number of special character
examples are ASCII code, EBCDIC code, Baudot code , Hollerith Code
(1)ASCII code:
It is called American standard Code for Information Interchange
It is a 7bit+1bit parity code system
It uses 7bit to code 128 characters and 1bit may be employed to indicate the parity of character
= total 128 character
For example letter A is represented in ASCII code as 1000001 + 1bit parity
(2) EBCDIC code:
It is called Extended Binary Coded Decimal Interchange Code
It uses 8bit for each character
= total 256 character
EBCDIC has same character symbol as ASCII code but bit assignment for character is different
(3) Baudot code:
It is a 5bit code
Baudot code represent 58 character with 5bit
(4) Hollerith Code:
In this code system information is coded with 12 bit
(5) Straight Binary code:
Only 2 symbols 1 and 0 are use to represent any digital information
(6) BCD code:
Full form of BCD is Binary Coded Decimal
In this code system each digit of a decimal number is represented by 4 bit binary equivalents
It is also called 8-4-2-1 code system
This is a weight code and arithmetic operation can be performed using this code
BCD code and Binary code for Decimal number 0 to 9 are exactly same
A disadvantage of BCD code system is , its required more number of bits to code a decimal number
An advantage of BCD code system is, it is very convenient and useful code for input and output operation in digital system
In table below Decimal and its Binary and BCD code is given
Decimal Binary BCD
0 0000 0000
1 0001 0001
2 0010 0010
3 0011 0011
4 0100 0100
5 0101 0101
6 0110 0110
7 0111 0111
8 1000 1000
9 1001 1001
Example: Convert Decimal number 150 to its BCD code
Solution: For converting Decimal number 150 to BCD code ,we have to write 4bit binary equivalent of each digit in given Decimal number
150 = 1 5 0
(0001)(0101)(0000) =000101010000 – BCD code of 150
Example: Convert Decimal number 8.1 to its BCD code
Solution:
8.1 = 8 . 1
(1000).(0001) = 1000.0001 –BCD code of 8.1
Example:Find the Deimal number represented by the following BCD code
(a) 10000100 (b) 00110011 (c) 10100 (d) 1000.0010
Solution: To convert a BCD code into Decimal code , Start at the decimal point(from most right hand side) and break the code into group of 4 bits binary. Then write the decimal digit represented by each 4 bit group of binary
BCD code 4bit grouping Decimal code
(a) 10000100 = (1000)(0100) = (8)(6)=86
(b) 00110011 = (0011)(0011) = (3)(3)=33
(c) 10100 = (1)(0100) =(0001)(0100) =(1)(4)=14
(d)1000.0010 = (1000).(0010) = (8).(2) = 8.2
(7) Excess-3 code:
It is an another form of BCD code system , in which each digit of decimal number is coded into 4bit binary number and to obtained Excess-3 code add 4bit binary code of decimal number 3 to each 4bit group BCD code
Example : Convert Decimal number 5 to Excess-3 code
Decimal number 5
BCD code 0101
Add 4bit binary of 3 0101
in above BCD code + 0011
Excess-3 code 1000
Another way to obtain Excess-3 code from a decimal code by adding 3 to each decimal digit and then convert the each digit of result in the group of 4 bit binary
Example: Convert each of the following decimal number to Exess-3 code
(a) 31 (b) 5112
Solution: (a) 31
Decimal number 3 1
Add 3 to each +3 +3
Digit
Result 6 4
4bit binary
Code of each (0110) (0100)
Digit
Excess-3 code 01100100
(b) 5112
Decimal number 5 1 1 2
Add 3 to each +3 +3 +3 +3
Digit
Result 8 4 4 5
4bit binary code (1000)(0100)(0100)(0101)
Of each digit
Excess-3 code 1000010001000101
Excess-3 code is self-complementing that means 1s complement of an Excess-3 number is the Excess-3 code for the 9s complement of corresponding decimal number
Example:
Excess -3 code for Decimal 3 is 0110
1s complement of 0110 is 1001 which is Excess-3 code of Decimal 6
Decimal 6 is the 9s complement of Decimal 3
Excess-3 code is an unweighted code which means that there is no specific weight assigned to the bit position
Excess-3 code is useful in some arithmetic operation because 9s complement is used for subtraction
(8) Gray Code:
Gray code is unweighted code which means that there is no specific weight assigned to the bit position
Gray Code is called “ Minimum change code” which means that this code Exhibits only a single bit change from one code number to next code and this is the advantage of Gray code over Binary code system
Gray code is not an Arithmetic code
Gray code can have any number of bits
Gray code is also known as Reflected code
MSB (most significant bit ) of gray code and Binary Code is always same
Decimal Number Binary code 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
From above gray code numbers it is clear that any number code is differ by one bit
Binary code to Gray code Conversion:
Example : Convert Binary code 10100 to Gray Code
Solution:
Step(1): 1 0 1 0 0 given Binary Code
1 Gray code
Step(2): 1 + 0 1 0 0 given Binary Code
1 1 Gray Code
Step(3): 1 0 + 1 0 0 given Binary Code
1 1 1 Gray Code
Step(4): 1 0 1 +0 0 given Binary Code
1 1 1 1 Gray Code
Step(5): 1 0 1 0 + 0 given Binary Code
1 1 1 1 0 Gray Code
Therefore Gray code for given binary code 10100 will be 11110
(9) Octal code:
It is 3-bit binary code
In octal code all octal decimal digit from 0 to 7 is coded into 3-bit straight binary number
Code for octal digit 5 will be 101
(10) Hexadecimal Code:
It is a 4-bit binary code
