BCD & Excess-3 Converter

BCD and Excess-3 Codes

BCD (Binary Coded Decimal) and Excess-3 are important binary codes used in digital systems for representing decimal numbers. Each has unique properties that make them suitable for different applications.

BCD (Binary Coded Decimal)

What is BCD?

BCD represents each decimal digit (0-9) using 4 binary bits. It's a weighted code where each bit position has a specific weight (8-4-2-1).

BCD Encoding Table

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

Excess-3 Code

What is Excess-3?

Excess-3 is an unweighted code obtained by adding 3 to each decimal digit before converting to binary. It's self-complementing, making arithmetic operations easier.

Excess-3 Encoding Table

Decimal	Excess-3	Decimal	Excess-3
0	0011	5	1000
1	0100	6	1001
2	0101	7	1010
3	0110	8	1011
4	0111	9	1100

Conversion Methods

Decimal to BCD

1. Take each decimal digit separately
2. Convert each digit to 4-bit binary
3. Concatenate the 4-bit groups

BCD to Excess-3

1. Take each 4-bit BCD group
2. Add 3 to the decimal value
3. Convert result to 4-bit binary

Properties and Advantages

BCD Properties

• Weighted code: 8-4-2-1 weights
• Easy conversion: Direct decimal-to-binary mapping
• Human readable: Each digit encoded separately
• No invalid codes: Uses only 10 of 16 possible combinations

Excess-3 Properties

• Self-complementing: 9's complement obtained by bit inversion
• Unweighted: No positional weights
• Arithmetic friendly: Easier addition/subtraction
• No zero code: Minimum code is 0011

Applications

BCD Applications

• Digital displays (7-segment)
• Calculators and meters
• Financial systems
• Real-time clocks

Excess-3 Applications

• Arithmetic circuits
• Early computers
• Error detection systems
• Complementary arithmetic

Examples

Example 1: Convert 247₁₀

• BCD: 2→0010, 4→0100, 7→0111 = 0010 0100 0111
• Excess-3: 2+3=5→0101, 4+3=7→0111, 7+3=10→1010 = 0101 0111 1010

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