Question

Convert (1011.11)2 into its decimal equivalent.

Answer 1

Answer:

What is 1011.11 binary in decimal? 1011.11 from binary to decimal is 11.75. Here we show you how to write 1011.112 in decimal and how to convert 1011.11 from base-2 to base-10.

Answer 2

The answer is 11.75

Given:  (1011.11)₂ is a binary number

To find: Convert (1011.11)₂ into decimal equivalent

Solution: To convert binary number into decimal number we need multiply each digit in binary number with corresponding power of 2

Example:

(101)₂ =  1×2² + 0×2¹ + 1×2⁰ = 1×8 + 0 + 1×1 = 8 + 1 = 9

⇒  (101)₂ = 9  (as decimal number)  

If there is a point in given number we will do it as given be below

(10.1)₂ = 1×2¹ + 0×2⁰ + 1 × 2⁻¹  = 2 + 1 + $\frac{1}{2}$ = 3 + 0.5 = 3.5

⇒ (10.1)₂ = 3.5   (as decimal number)  

⇒ (1011.11)₂  = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ + 1 × 2⁻¹ + 1 × 2⁻²  

= 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 + 1 × $\frac{1}{2}$ + 1 × $\frac{1}{2^{2} }$  

= 8 + 0 + 2 + 1 + $\frac{1}{2}$ + $\frac{1}{4 }$  

= 11 + 0.5 + 0.25  = 11.75  

Therefore, (1011.11)₂ = 11.75   (as decimal number)  

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