Compute (110110001.01)2 + (27.12)10 + (121.25)16 – (130.20)16 and display the answer in hexadecimal base.

(110110001.01)₂ + (27.12)₁₀ + (121.25)₁₆ – (130.20)₁₆ = (445.38953125)₁₀ = (1BD.63B851EB851EB851EB85)₁₆

Explanation:

(110110001.01)₂ + (27.12)₁₀ + (121.25)₁₆ – (130.20)₁₆

leaving the answer in hexadecimal

To solve this, we first convert all the numbers to base 10, solve, then convert back to hexadecimal

(110110001.01)₂ = (1×2⁸) + (1×2⁷) + (0×2⁶) + (1×2⁵) + (1×2⁴) + (0×2³) + (0×2²) + (0×2¹) + (1×2⁰) + (0×2⁻¹) + (1×2⁻²) = (433.25)₁₀

(27.12)₁₀ = (27.12)₁₀

(121.25)₁₆ = (1×16²) + (2×16¹) + (1×16⁰) + (2×16⁻¹) + (5×16⁻²) = (289.14453125)₁₀

(130.20)₁₆ = (1×16²) + (3×16¹) + (0×16⁰) + (2×16⁻¹) + (0×16⁻²) = (304.125)₁₀

(110110001.01)₂ + (27.12)₁₀ + (121.25)₁₆ – (130.20)₁₆

= (433.25)₁₀ + (27.12)₁₀ + (289.14453125)₁₀ - (304.125)₁₀

= (445.38953125)₁₀

We then convert (445.38953125)₁₀ back to hexadecimal

(445.38953125)₁₀ = (1BD.63B851EB851EB851EB85)₁₆

16 | 445 | R

16 | 27 | 13 = D

16 | 1 | 11 = B

16 | 0 | 1 = 1

Read upwards, 1BD

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