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Number conversions (10111.101)2 etc.

Short answer

i) 10111.101 binary = 23.625 decimal (sum of powers). ii) AFC.00 hex to octal via binary: 5374. iii) 901 BCD: 1001 0000 0001.

Perform the conversion of the following: i) (10111.101)2 = (?)10 ii) (AFC.00)16 = (?)8 iii) (901)10 = (?)BCD

i) (10111.101)₂ to decimal

Integer: 1×16 + 0×8 + 1×4 + 1×2 + 1×1 = 23 Fraction: 1×0.5 + 0×0.25 + 1×0.125 = 0.625

(10111.101)₂ = (23.625)₁₀

ii) (AFC.00)₁₆ to octal

A    F    C   .  0    0
1010 1111 1100 . 0000 0000

Integer: 101 011 111 100  = 5 3 7 4
Fraction: 000 000 00(0)   = 0 0 0

(AFC.00)₁₆ = (5374)₈, since the fractional part is zero.

iii) (901)₁₀ to BCD

9 = 1001, 0 = 0000, 1 = 0001

(901)₁₀ = (1001 0000 0001)BCD

✓ Answer checked by Claude Opus 5.5 (high effort)

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