8421 Method for Binary and Decimal Conversion
Understanding the 8421 Strategy for Binary and Decimal Conversion
The 8421 strategy, also known as the weighted binary system, is a method to convert binary numbers to decimalusing the positional values of powers of 2. The numbers 8, 4, 2, and 1 represent the weights assigned to each position in a 4-bit binary number.
1. 8421 Strategy for Binary to Decimal Conversion
Each digit in a 4-bit binary number has a specific weight based on the powers of 2:
| Binary Digit | Weight |
|---|---|
| 2³ (8) | 8 |
| 2² (4) | 4 |
| 2¹ (2) | 2 |
| 2⁰ (1) | 1 |
Example 1: Convert 1101₂ to Decimal Using 8421
Binary Number: 1101₂
- Multiply each binary digit by its corresponding 8421 weight:(1×8)+(1×4)+(0×2)+(1×1)(1×8)+(1×4)+(0×2)+(1×1)
- Perform the calculations:8+4+0+1=138+4+0+1=13
Final Answer: 1101₂ = 13₁₀
2. 8421 Strategy for Decimal to Binary Conversion
The 8421 code also helps convert decimal to binary by checking which weights add up to the decimal number.
Example 2: Convert 9₁₀ to Binary Using 8421
- Find which weights (8, 4, 2, 1) add up to 9:
- 8 is included → 1
- 4 is not included → 0
- 2 is not included → 0
- 1 is included → 1
- Write the binary number:
9₁₀ = 1001₂
3. More Examples
| Decimal | Binary (8421 Code) |
|---|---|
| 3 | 0011₂ |
| 5 | 0101₂ |
| 7 | 0111₂ |
| 10 | 1010₂ |
| 12 | 1100₂ |
| 15 | 1111₂ |
MCQs on 8421 Strategy
1. What is the decimal equivalent of 1010₂ using the 8421 strategy?
a) 8
b) 9
c) 10
d) 11
✅ Answer: c) 10
2. Which binary number represents 6 using the 8421 strategy?
a) 0110₂
b) 0100₂
c) 1100₂
d) 1010₂
✅ Answer: a) 0110₂
3. Which decimal number does the binary 1001₂ represent?
a) 7
b) 8
c) 9
d) 10
✅ Answer: c) 9
4. In the 8421 strategy, what weight does the rightmost binary digit (LSB) represent?
a) 1
b) 2
c) 4
d) 8
✅ Answer: a) 1
5. Convert decimal 13 to binary using 8421 strategy.
a) 1000₂
b) 1101₂
c) 1011₂
d) 1111₂
✅ Answer: b) 1101₂
The 8421 strategy simplifies binary-to-decimal and decimal-to-binary conversions by focusing on weights (8, 4, 2, 1). Let me know if you want more practice questions! 🚀
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