1.1 Data Representation: BCD and Hexadecimal

This section explores practical applications of Binary Coded Decimal (BCD) and Hexadecimal number systems. Understanding these representations is crucial for working with data in various computer systems and embedded applications.

Binary Coded Decimal (BCD)

BCD is a method of representing decimal digits using binary. Each decimal digit is represented by a 4-bit binary code, with 0 to 9 assigned the codes 0000 to 1010 respectively. This allows for direct conversion between decimal and binary values without the need for complex calculations.

Practical Applications of BCD

• Digital Clocks and Displays: BCD is commonly used to display decimal numbers on digital clocks, calculators, and other displays. The BCD representation is directly converted to the appropriate 7-segment or LED patterns for visual output.
• Financial Systems: In some financial systems, BCD is used to represent currency values. This simplifies calculations and reduces the risk of errors associated with floating-point arithmetic.
• Industrial Control Systems: BCD can be found in industrial control systems for reading and displaying sensor values that are naturally represented in decimal form.
• Legacy Systems: Older computer systems often used BCD for data storage and processing due to its simplicity and compatibility with hardware.

Decimal Digit	BCD Code
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

Hexadecimal

Hexadecimal (hex) is a base-16 number system. It uses 16 symbols to represent values: 0-9 and A-F, where A=10, B=11, C=12, D=13, E=14, and F=15. Hexadecimal is a compact and convenient way to represent binary data.

Practical Applications of Hexadecimal

• Memory Addressing: Hexadecimal is frequently used to represent memory addresses in computer systems. It provides a more concise way to express large binary addresses. For example, the memory address $1000$ in hexadecimal is equivalent to the binary $000100000000$.
• Color Codes: In web development and graphics, hexadecimal is used to represent colors. Each color component (e.g., red, green, blue) is typically represented by a 2-digit hexadecimal code. For instance, the color white is represented as #FFFFFF.
• Data Storage and File Formats: Hexadecimal is used to represent binary data in file formats, such as image files, audio files, and executable programs. This allows for easy inspection and manipulation of the raw data.
• Networking: Hexadecimal is used in networking to represent IP addresses, MAC addresses, and other network-related data.
• Programming: Hexadecimal is often used in programming to represent numerical constants, color values, and memory addresses.

Decimal Value	Hexadecimal Value
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	A
11	B
12	C
13	D
14	E
15	F