1. Combine the binary representations: 0101 0111 0011

2. Convert each digit to binary:
• 5 -> 0101
• 7 -> 0111
• 3 -> 0011

3. Separate each digit: 5, 7, 3

Example Conversion

• Digital meters: Used in devices like electricity meters where the numerical data needs to be displayed accurately.

• Calculators: BCD allows for easy conversion between the number as displayed and the number as processed internally.

• Digital clocks: Each digit of the time is represented in BCD and then displayed.

BCD in Digital Systems

• Subtraction: Similar to addition, but adjustments are made by subtracting 6 if needed.

• Addition: When adding BCD numbers, if a digit exceeds 9, an adjustment is made by adding 6 (0110 in binary) to correct the result. For example, adding 7 (0111) and 5 (0101):
• Binary addition: 0111 + 0101 = 1100 (12 in decimal)
• Since the result exceeds 9, add 6: 1100 + 0110 = 10010
• The final result is 0010 (2) with a carry of 1 to the next digit.

BCD Arithmetic

• Complexity in Arithmetic: Arithmetic operations on BCD numbers can be more complex and slower compared to binary arithmetic due to the need for adjustments after each operation.

• Inefficiency in Storage: BCD is less space-efficient compared to pure binary representation since it uses more bits to represent a number. For instance, representing the decimal number 99 in binary requires 7 bits (1100011), while in BCD it requires 8 bits (1001 1001).

Disadvantages of BCD

• Accuracy: BCD avoids the rounding errors that can occur in binary floating-point representations.

• Decimal Arithmetic: Performing arithmetic operations on BCD numbers can be more intuitive for applications where humans interact with the system, such as calculators and digital clocks.

• Ease of Conversion: Converting a decimal number to BCD and vice versa is straightforward since each decimal digit is handled independently.

Advantages of BCD

1. Unpacked BCD: Each byte contains one BCD digit. For example, the decimal number "92" would be represented in two bytes: 00001001 00000010.

2. Packed BCD: Each byte contains two BCD digits. For example, the decimal number "92" would be represented in one byte as 10010010.

Types of BCD

BCD Representation

• For example, the decimal number "92" is represented in BCD as:
• 9 in decimal is 1001 in binary
• 2 in decimal is 0010 in binary
• Thus, "92" in BCD is 1001 0010

• In BCD, each decimal digit (0-9) is represented by a fixed number of binary digits, typically four.

Basics of BCD