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Number conversions (25.5)10, (EAB)16

Short answer

(a) Integer 25 to binary by repeated division gives 11001, fraction 0.5×2=1.0 → .1, so (11001.1)₂. (b) EAB hex: 14×256+10×16+11 = 3755. (c) 9180 BCD: 1001 0001 1000 0000.

Convert the following number system. (a) (25.5)10 = (?)2 (b) (EAB)16 = (?)10 (c) (9180)10 = (?)BCD

(a) (25.5)₁₀ to binary

Integer 25: divide by 2 repeatedly. 25 → 12 r1, 12 → 6 r0, 6 → 3 r0, 3 → 1 r1, 1 → 0 r1. Read upwards: 11001. Fraction 0.5 × 2 = 1.0, so the fraction is .1.

(25.5)₁₀ = (11001.1)₂

(b) (EAB)₁₆ to decimal

E = 14, A = 10, B = 11. 14 × 16² + 10 × 16 + 11 = 3584 + 160 + 11 = 3755

(EAB)₁₆ = (3755)₁₀

(c) (9180)₁₀ to BCD

Write each decimal digit as a 4-bit binary number: 9 = 1001, 1 = 0001, 8 = 1000, 0 = 0000

(9180)₁₀ = (1001 0001 1000 0000)BCD

✓ Answer checked by Claude Opus 5.5 (high effort)

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