<<–2/”>a href=”https://exam.pscnotes.com/5653-2/”>h2>BCD: Binary-Coded Decimal
What is BCD?
Binary-Coded Decimal (BCD) is a system for representing decimal numbers (0-9) using binary digits (0 and 1). In BCD, each decimal digit is represented by its equivalent 4-bit binary code. This differs from the standard binary representation where numbers are represented in base-2.
How BCD Works
In BCD, each decimal digit is encoded using a 4-bit binary code, as shown in the table below:
| Decimal Digit | BCD Code |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
For example, the decimal number 25 would be represented in BCD as:
- 2: 0010
- 5: 0101
Therefore, the BCD representation of 25 is 0010 0101.
Advantages of BCD
- Easy Conversion: BCD makes it easy to convert between decimal and binary representations.
- Human Readability: BCD codes are easily understood by humans as they directly correspond to decimal digits.
- Arithmetic Operations: Arithmetic operations like addition and subtraction can be performed directly on BCD numbers without the need for complex conversions.
- Decimal Point Handling: BCD can easily represent decimal points by adding a separate code for the decimal point.
Disadvantages of BCD
- Space Inefficiency: BCD requires more bits to represent a number compared to pure binary representation. For example, representing the number 15 in binary requires only 4 bits (1111), while BCD requires 8 bits (0001 0101).
- Limited Range: BCD can only represent numbers up to 9999 using a single byte (8 bits).
- Complex Hardware: Implementing BCD arithmetic operations requires specialized hardware circuits.
Applications of BCD
- Digital Clocks and Timers: BCD is widely used in digital clocks and timers for displaying time and date information.
- Calculators: Many calculators use BCD to represent numbers and perform arithmetic operations.
- Data Acquisition Systems: BCD is used in data acquisition systems for storing and processing data from sensors and other devices.
- Financial Transactions: BCD is used in financial systems for representing monetary values and performing calculations.
BCD Arithmetic
Addition:
BCD addition is similar to binary addition, but with an additional step to ensure that the result is a valid BCD code. If the sum of two BCD digits exceeds 9, a correction factor of 6 (0110) is added to the result.
Example:
Add the BCD numbers 0101 (5) and 0011 (3).
- Binary Addition: 0101 + 0011 = 1000
- Correction: Since the result (1000) is greater than 9, add 0110 to it: 1000 + 0110 = 1110
- Final BCD Result: 1110 (14)
Subtraction:
BCD subtraction is similar to binary subtraction, but with an additional step to ensure that the result is a valid BCD code. If the minuend (the number being subtracted from) is smaller than the subtrahend (the number being subtracted), a borrow is required.
Example:
Subtract the BCD number 0011 (3) from 0101 (5).
- Binary Subtraction: 0101 – 0011 = 0010
- Final BCD Result: 0010 (2)
Packed and Unpacked BCD
BCD can be implemented in two ways:
- Packed BCD: Each byte represents two decimal digits.
- Unpacked BCD: Each byte represents a single decimal digit.
Packed BCD:
- Advantages: More efficient use of memory space.
- Disadvantages: More complex hardware for arithmetic operations.
Unpacked BCD:
- Advantages: Simpler hardware for arithmetic operations.
- Disadvantages: Less efficient use of memory space.
Table: Packed vs. Unpacked BCD
| Feature | Packed BCD | Unpacked BCD |
|---|---|---|
| Bits per decimal digit | 4 | 8 |
| Memory efficiency | High | Low |
| Hardware complexity | High | Low |
| Example | 0010 0101 (25) | 0000 0101 (5) |
Table: BCD Codes for Decimal Digits
| Decimal Digit | BCD Code |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
Frequently Asked Questions (FAQs)
Q: What is the difference between BCD and binary?
A: BCD represents decimal numbers using 4-bit binary codes, while binary represents numbers directly in base-2.
Q: What are the advantages of using BCD?
A: BCD offers advantages like easy conversion to decimal, human readability, and simplified arithmetic operations.
Q: What are the disadvantages of using BCD?
A: BCD is space-inefficient, has a limited range, and requires complex hardware for arithmetic operations.
Q: What are some applications of BCD?
A: BCD is used in digital clocks, calculators, data acquisition systems, and financial transactions.
Q: What is the difference between packed and unpacked BCD?
A: Packed BCD stores two decimal digits per byte, while unpacked BCD stores one decimal digit per byte.
Q: How is BCD addition performed?
A: BCD addition is similar to binary addition, but with a correction factor of 6 added if the sum exceeds 9.
Q: How is BCD subtraction performed?
A: BCD subtraction is similar to binary subtraction, but with a borrow required if the minuend is smaller than the subtrahend.