1.7 Binary Codes

Digital systems operate using binary code, a system of 1s and 0s. However, humans interact with information using decimal numbers. To bridge this gap, digital devices must convert data between binary and a more human-readable format. This involves representing each character (number, letter, or symbol) as a unique combination of 1s and 0s. This representation is called a code.

Part 1.7.1 Binary Coded Decimals (BCD) Codes

Arithmetic operations are typically performed using decimal numbers. However, computers work with binary numbers. Binary Coded Decimal (BCD) was developed to bridge this gap. BCD represents each decimal digit as a four-bit binary equivalent. Numbers 0 to 9 correspond to binary codes 0000 to 1001. Six combinations (1010 to 1111) remain unused. BCD codes are categorized into weighted and unweighted types.

Example No. 1

Convert 936 to BCD Code

Solution:

	3^rd Digit	2^nd Digit	1^st Digit
	9	3	6
Answer	1001	0011	0110

Example No. 2

Convert 7121 to BCD Code

Solution:

	4^th Digit	3^rd Digit	2^nd Digit	1^st Digit
	7	1	2	1
Answer	0111	0001	0010	0001

Part 1.7.2 Weighted BCD Code

The most common weighted BCD code is the 8-4-2-1 code. In this code, the digits in a binary number have weights of 8, 4, 2, and 1. The table below shows several weighted BCD codes.

Decimal Digit	Natural Binary 8-4-2-1	4-2-2-1	2-4-2-1		Biquianary
					5-0		4-3-2-1-0
0	0000	0000		0000		01		00001
1	0001	0001		0001		01		00010
2	0010	0010		0010		01		00100
3	0011	0011		0110		01		01000
4	0100	1000		0100		01		10000
5	0101	0111		1011		01		00001
6	0110	1100		1100		10		00010
7	0111	1101		1101		10		00100
8	1000	1110		1110		10		01000
9	1001	1111		1111		10		10000

Part 1.7.3 Unweighted BCD Code

Unweighted BCD codes are used in data processing, transmission, and measurement, but not in arithmetic operations due to their lack of positional weight. Examples include Excess-3 code, Gray code, and 2 out of 5 code. The table below shows these codes.

Decimal Digit	Excess-3 Code	Gray Code	2 out of 5
0	0011	0000	00011
1	0100	0001	00101
2	0101	0011	00110
3	0110	0010	01001
4	0111	0110	01010
5	1000	0111	01100
6	1001	0101	10001
7	1010	0100	10010
8	1011	1100	10100
9	1100	1101	1100

Note: Excess-3 code is always three greater than the same 8-4-2-1 representation.

Part 1.7.4 Character Codes

In addition to numbers, digital systems must handle text, symbols, and other non-numeric information. To do this, they use character codes that represent letters, punctuation marks, and special characters.

EBCDIC: An 8-bit code used in IBM systems. It represents characters using two 4-bit groups.

ASCII: The most common character code. It's a 7-bit code divided into data link control, graphic control, and alphanumeric characters. Used for data transfer between computers and devices.

Baudot Code: A 5-level code developed for teletype machines. Represents letters, numbers, punctuation, and special symbols using a "lowercase" and "uppercase" set.

Hollerith Code: Used in punched cards. Each column represents a digit, letter, or symbol. A 12-level code is used to represent data.

Part 1.7.5 Codes for Actions, Conditions, and States

These codes use simple binary numbers to control actions, indicate conditions, or represent the current state of hardware in a digital system.

Part 1.7.6 Codes for Detecting and Correcting Errors

When transmitting binary data, errors can occur, leading to misinterpretation. To address this, digital systems use error detection and correction methods. Parity bits, checksum codes, CRC codes, and Hamming codes are examples of these techniques.

Part 1.7.7 Codes for Data Transmission

Data transmission is a common operation in digital systems. Information is transmitted in binary form as voltage levels between sending and receiving circuits. The format of the signal on the line during transmission is determined by the line code. Manchester code and AMI are examples of line codes used for data transmission.