| Weighted Binary Systems |
Weighted binary codes are those which obey the positional weighting principles, each position of the number represents a specific weight. The binary counting sequence is an example. |
| Decimal | 8421 | 2421 | 5211 | Excess-3 | | 0 | 0000 | 0000 | 0000 | 0011 | | 1 | 0001 | 0001 | 0001 | 0100 | | 2 | 0010 | 0010 | 0011 | 0101 | | 3 | 0011 | 0011 | 0101 | 0110 | | 4 | 0100 | 0100 | 0111 | 0111 | | 5 | 0101 | 1011 | 1000 | 1000 | | 6 | 0110 | 1100 | 1010 | 1001 | | 7 | 0111 | 1101 | 1100 | 1010 | | 8 | 1000 | 1110 | 1110 | 1011 | | 9 | 1001 | 1111 | 1111 | 1100 | |
| 8421 Code/BCD Code |
The BCD (Binary Coded Decimal) is a straight assignment of the binary equivalent. It is possible to assign weights to the binary bits according to their positions. The weights in the BCD code are 8,4,2,1. |
Example: The bit assignment 1001, can be seen by its weights to represent the decimal 9 because: |
1x8+0x4+0x2+1x1 = 9 |
| 2421 Code |
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 four bits weight is 2 + 4 + 2 + 1 = 9. Hence the 2421 code represents the decimal numbers from 0 to 9. |
| 5211 Code |
This is a weighted code, its weights are 5, 2, 1 and 1. A decimal number is represented in 4-bit form and the total four bits weight is 5 + 2 + 1 + 1 = 9. Hence the 5211 code represents the decimal numbers from 0 to 9. |
| Reflective Code |
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. |
| Sequential Codes |
A code is said to be sequential when two subsequent codes, seen as numbers in binary representation, differ by one. This greatly aids mathematical manipulation of data. The 8421 and Excess-3 codes are sequential, whereas the 2421 and 5211 codes are not. |
| Non Weighted Codes |
Non weighted codes are codes that are not positionally weighted. That is, each position within the binary number is not assigned a fixed value. |
| Excess-3 Code |
Excess-3 is a non weighted code used to express decimal numbers. The code derives its name from the fact that each binary code is the corresponding 8421 code plus 0011(3). |
Example: 1000 of 8421 = 1011 in Excess-3 |
| Gray Code |
The gray code belongs to a class of codes called minimum change codes, in which only one bit in the code changes when moving from one code to the next. The Gray code is non-weighted code, as the position of bit does not contain any weight. The gray code is a reflective digital code which has the special property that any two subsequent numbers codes differ by only one bit. This is also called a unit-distance code. In digital Gray code has got a special place. |
| 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 | | 9 | 1001 | 1101 | | 10 | 1010 | 1111 | | 11 | 1011 | 1110 | | 12 | 1100 | 1010 | | 13 | 1101 | 1011 | | 14 | 1110 | 1001 | | 15 | 1111 | 1000 | |
| Binary to Gray Conversion |
- Gray Code MSB is binary code MSB.
- Gray Code MSB-1 is the XOR of binary code MSB and MSB-1.
- MSB-2 bit of gray code is XOR of MSB-1 and MSB-2 bit of binary code.
- MSB-N bit of gray code is XOR of MSB-N-1 and MSB-N bit of binary code.
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