How to Convert Binary Numbers into Decimal Numbers
The binary to decimal conversion involves multiplying each binary digit by powers of 2 and summing the results.
Steps for Binary to Decimal Conversion
- Write the binary number.
- Assign powers of 2, starting from 0 (rightmost digit).
- Multiply each binary digit by 2 raised to its position.
- Sum all the results to get the decimal equivalent.
Example 1: Convert 1011₂ to Decimal
Step-by-step Calculation
Binary Number: 1011₂
(1×23)+(0×22)+(1×21)+(1×20)(1×23)+(0×22)+(1×21)+(1×20)(1×8)+(0×4)+(1×2)+(1×1)(1×8)+(0×4)+(1×2)+(1×1)8+0+2+1=11108+0+2+1=1110
Final Answer: 1011₂ = 11₁₀
Example 2: Convert 11010₂ to Decimal
Binary Number: 11010₂
(1×24)+(1×23)+(0×22)+(1×21)+(0×20)(1×24)+(1×23)+(0×22)+(1×21)+(0×20)(1×16)+(1×8)+(0×4)+(1×2)+(0×1)(1×16)+(1×8)+(0×4)+(1×2)+(0×1)16+8+0+2+0=261016+8+0+2+0=2610
Final Answer: 11010₂ = 26₁₀
MCQs on Binary to Decimal Conversion
1. What is the decimal equivalent of 1001₂?
a) 7
b) 8
c) 9
d) 10
✅ Answer: c) 9
2. What is the decimal equivalent of 1110₂?
a) 12
b) 13
c) 14
d) 15
✅ Answer: c) 14
3. The binary number 10100₂ is equal to which decimal number?
a) 18
b) 20
c) 22
d) 24
✅ Answer: b) 20
4. Convert 1101₂ into decimal.
a) 11
b) 12
c) 13
d) 14
✅ Answer: c) 13
5. The decimal equivalent of 100000₂ is:
a) 16
b) 32
c) 64
d) 128
✅ Answer: b) 32
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