Question

Convert the following binary numbers to decimal numbers.
a. 10110.111^2
b. 1001111.11^2
c. 1101111^2
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Answer 1

Answer:

A.(10110.111)₂ = (22.875)₁₀

B.(1001111.11)₂ = (79.75)₁₀

C.(1101111)₂ = (111)₁₀

Explanation:

A.(10110.111)₂ = (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) + (1 × 2⁻¹) + (1 × 2⁻²) + (1 × 2⁻³) = (22.875)₁₀

B.(1001111.11)₂ = (1 × 2⁶) + (0 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰) + (1 × 2⁻¹) + (1 × 2⁻²) = (79.75)₁₀

C.(1101111)₂ = (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰) = (111)₁₀