Binary Codes Tutorial with Examples in Switching Theory and Computer
Binary codes are codes which are represented in binary system with modification from original ones.
Weighted Binary System
Weighted binary codes are those which obey the positional weighting principles, each position of a number represents a specific weight.
e.g., 8421, 2421, 5211.
A code is said to be sequential when two subsequent codes, seen as numbers in binary representation, differ by one. The 8421 and excess-3 codes are sequential, whereas 2421 and 5211 codes are not.
Non-weighted codes are codes that are not positionally weighted. That is each position within the binary number is not assigned a fixed value.
A code is said to be reflective when code for 9 is complement for the code for 0 and so is for 8 and 1 codes, 7 and 2, 6 and 3, 5 and 4. Codes 2421, 5211 and excess-3 are reflective, whereas the 8421 code is not.
BCD (Binary Coded Decimal)
it is a straight assignment of the binary equivalent. To encode a decimal number using the common BCD encoding. Each decimal digit is stored in a 4-bit number.
BCD encoding for number 127 would be
1 2 7
(0001 0010 0111)–> BCD equivalent of 127 whereas the pure binary number would be (01111111)2
Add (148 + 157) =?
When sum of 2 digits is greater than or equal to 9, then we need to add 6 i.e., 0110.
This is a weighted code, its weights are 2,4,2 and 1. A decimal number is represented in 4 bit form and the total 4 bits weight is
2 + 4 + 2 + 1= 9.
Hence, 2421 code represents the decimal numbers from 0 to 9.
Excess- 3 is a non-weighted code used to represent decimal numbers. The code derive its name from the fact that each binary code is the corresponding 8421 code plus 0011(3).
e.g., Decimal 8421 Excess – 3
8 1000 1000+0011-1011
6 0110 0110+0011 1001
This is a variable weighted code and is cyclic. This means that it is arranged, so that every transition from one value to the next value involves only one bit change.
Binary to Gray Code Conversion
- Write down the number in binary codes.
- The Most Significant Bit (MSB) of the .gray code will be same as the MSB of binary coo
- Perform XOR operation on MSB and next bit to the MSB in binary number.
- Repeat step 3 till all bits of binary number have been XOR operation, the resultant code ;s: the gray code equivalent to binary code.
Gray Code to Binary Conversion
1. Start with the MSB of gray/ coded =number.
- Copy this bit as the MSB of the binary number.
- Now., perform Ex-OR operation of this bit with the next bit of the binary number.
- Repeat step 3 till all bits of gray coded number have been used in XOR operation. The resultant number is the binary equivalent of the gray number.
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