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3 years ago

Find octal expansion of (B5D)16.

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

b5d₁₆ = 11×16² + 5×16¹ + 13×16⁰

… = 11×(2×8)² + 5×(2×8)¹ + 13×(2×8)⁰

… = 11×4×8² + 5×2×8¹ + 13×8⁰

… = 44×8² + 10×8¹ + 13×8⁰

… = (40 + 4)×8² + (8 + 2)×8¹ + (8 + 5)×8⁰

… = (5×8 + 4)×8² + (1×8 + 2)×8¹ + (1×8 + 5)×8⁰

… = 5×8³ + 4×8² + 1×8² + 2×8¹ + 1×8¹ + 5×8⁰

… = 5×8³ + 5×8² + 3×8¹ + 5×8⁰

… = 5535₈

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