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

  1. Write the binary number.
  2. Assign powers of 2, starting from 0 (rightmost digit).
  3. Multiply each binary digit by 2 raised to its position.
  4. 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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