Types of binary codes

Binary codes are codes which are generally represented in binary system with modification from the original ones. They are stated as follows following: Weighted codes and Non-Weighted codes

Weighted binary codes:

Weighted binary codes are those codes which obey the positional weighting principles, each position of number represents a particular weight. The binary counting sequence is the example.

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 binary equivalent. It is possible to assign weights to binary bits according to their positions. The weights in BCD code are 8,4,2,1.

Example: The bit assignment 1001, can be seen by the weights of it to represent the decimal 9 as 1x8+0x4+0x2+1x1 = 9

2421 code

This is a weighted code; the weights of it are 2, 4, 2 and 1. A decimal number can be represented in 4-bit form and total four bits weight is 2 + 4 + 2 + 1 = 9. Hence 2421 code represents the decimal numbers from 0 to 9.

5211 code

It is a weighted code; the weights of it are 5, 2, 1 and 1. A decimal number is represented in 4-bit form and the total 4 bits weight is 5 + 2 + 1 + 1 = 9. Thus 5211 code shows 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 code

A code is sequential when the 2 subsequent codes, seen as numbers in binary representation, vary by one. This helps in mathematical manipulation of data. The 8421 and Excess-3 codes are sequential, while the 2421 and

5211 codes are not. Non-Weighted code

Non weighted codes are codes which are not weighted positionally. Which means that, each position within the binary number is not assigned a permanent value.

Excess-3 code

Excess-3 is a non weighted code which is used to express decimal numbers. The code obtains name of it from the fact that each binary code is 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 known as minimum change codes, in which just one bit in the code changes when moving from one code to other. The Gray code is non-weighted code, as position of the bit does not contain any weight. It is a reflective digital code which has the special property that any 2 subsequent numbers codes differ by just one bit. This is also known as unit-distance code. In the digital Gray code has got a significant place.

Error detecting and correcting codes

For the reliable transmission and storage of digital data, error detection and correction is needed. Below are the few examples of codes which allows error detection and error correction after the detection.

Error detecting codes

When the digital data is transmitted from one point to other, similar to in wireless transmission, or it is just stored, like in hard disks and memories, there are chances that data can get corrupted. To detect the data errors, we use special codes, which are error detection codes.

Parity bit

In the parity codes, every data byte, or nibble is checked if they have even number of one's or even number of zeros. Based on information an additional bit is appended to original data. Hence if we consider 8-bit data, adding parity bit will make it 9 bit long.

At  the  receiver  side,  once  again  parity  can be  computed  and  matched  with  the received parity (bit 9), and if they match, data is ok, else data is corrupt.

Two types of parity

Even parity: It checks if there is an even number of ones; if so, parity bit is zero. When the number of ones is odd then the parity bit is set to 1.

Odd Parity: It checks if there is an odd number of ones; if so, parity bit is zero. When the number of ones is even then the parity bit is set to 1.

Error correcting codes

Error correcting codes not only detect errors, but correct them also. This is used usually in the Satellite communication, where turn around delay is quite high as is the probability of data getting damage.

Hamming codes

Hamming code adds the minimum number of bits to data transmitted in a noisy channel, capable correct every possible one-bit error. It can detect two-bit errors and cannot distinguish in between 1-bit and 2-bits inconsistencies. It can't - in general - detect 3(or more)-bits errors.

Alphanumeric codes

The binary codes which can be used to represent all letters of the alphabet, punctuation marks, numbers and mathematical symbols, are called as alphanumeric codes or character codes. These codes facilitate us to interface the input-output devices such as the printers, keyboard, video displays with the computer.

ASCII codes

ASCII stands for the American Standard Code for Information Interchange. It has become a world standard alphanumeric code for the microcomputers and computers. It is a 7-bit code showing 27 = 128 different characters. These characters shows 26 upper case letters (A to Z), 26 lowercase letters (a to z), 10 numbers (0 to 9), the 33 special characters and symbols and 33 control characters.

EBCDIC codes

EBCDIC means Extended Binary Coded Decimal Interchange. It is basically used with large computer systems such as mainframes. EBCDIC is an 8-bit code and hence accommodates up to 256 characters. An EBCDIC code can be divided into 2 portions: 4 zone bits (on left) and 4 numeric bits (on right).

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