- 2071 Bhadra · 1×3 marks
Number conversions (10101.101)2 etc.
Short answer
(a) 1×16+0+1×4+0+1=21, fraction 0.5+0.125=0.625 → 21.625. (b) 9001180 BCD: 1001 0000 0000 0001 0001 1000 0000. (c) Hex to binary then groups of three: (1253.274)₈.
(a) (10101.101)2 = (?)10 (b) (9001180)10 = (?)BCD (c) (2AB.5E)16 = (?)8
(a) (10101.101)₂ to decimal
Integer: 1×16 + 0×8 + 1×4 + 0×2 + 1×1 = 21 Fraction: 1×2⁻¹ + 0×2⁻² + 1×2⁻³ = 0.5 + 0.125 = 0.625
(10101.101)₂ = (21.625)₁₀
(b) (9001180)₁₀ to BCD
9 = 1001, 0 = 0000, 0 = 0000, 1 = 0001, 1 = 0001, 8 = 1000, 0 = 0000
(9001180)₁₀ = (1001 0000 0000 0001 0001 1000 0000)BCD
(c) (2AB.5E)₁₆ to octal
Convert each hex digit to 4 bits, then regroup in 3 bits.
2 A B . 5 E
0010 1010 1011 . 0101 1110
Integer: 001 010 101 011 = 1 2 5 3
Fraction: 010 111 100 = 2 7 4 (padded with a zero)
(2AB.5E)₁₆ = (1253.274)₈
✓ Answer checked by Claude Opus 5.5 (high effort)
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