Question

Express the following numbers in decimal:

(a) (11001.1011)
2

(b) (A3.C)
16

(c) (75.16)
8

(d) (ABCD)
16

Answer 1

(a)

11001.1011₂ = 1×2⁴ + 1×2³ + 1×2⁰ + 1×2 ⁻¹ + 1×2 ⁻³ + 1×2 ⁻⁴

… = 16 + 8 + 1 + 1/2 + 1/8 + 1/16

… = 411/16

(b) In base 16, we have A₁₆ = 10 and C₁₆ = 12, so

A3.C₁₆ = 10×16¹ + 3×16⁰ + 12×16 ⁻¹

… = 160 + 3 + 12/16

… = 2620/16 = 655/4

(c)

75.16₈ = 7×8¹ + 5×8⁰ + 1×8 ⁻¹ + 6×8 ⁻²

… = 56 + 5 + 1/8 + 6/64

… = 3918/64 = 1959/32

(d) B₁₆ = 11 and D₁₆ = 13, so

ABCD₁₆ = 10×16³ + 11×16² + 12×16¹ + 13×16⁰

… = 40960 + 2816 + 192 + 13

… = 43981