1.Why can’t computers use decimal directly instead of binary?
2.Convert 156 to octal and verify using binary.
3.Convert 255 to hexadecimal and explain each step.
4.Convert binary 11100 to decimal, then to hexadecimal.
5.Convert octal 75 to binary, then to decimal for verification.
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1.
Answer: Computers rely on binary because their hardware uses two-state transistors (on/off), which align with 0 and 1, not the 10 states needed for decimal.
Description: Decimal requires complex multi-state circuits, while binary simplifies design and computation in digital systems.
Description: Decimal requires complex multi-state circuits, while binary simplifies design and computation in digital systems.
2.
Answer: 156 in octal is 234. In binary: 10011100, grouped as 010 011 100 = 2 3 4.
Description: Divide 156 by 8: 19 remainder 4, 2 remainder 3, 0 remainder 2 = 234. Binary check confirms accuracy.
Description: Divide 156 by 8: 19 remainder 4, 2 remainder 3, 0 remainder 2 = 234. Binary check confirms accuracy.
3.
Answer: 255 in hex is FF.
Description: 255 ÷ 16 = 15 remainder 15. 15 = F, so 15F = FF. Each digit represents a power of 16 (F × 16¹ + F × 16⁰).
Description: 255 ÷ 16 = 15 remainder 15. 15 = F, so 15F = FF. Each digit represents a power of 16 (F × 16¹ + F × 16⁰).
4.
Answer: Binary 11100 = 28 (decimal), 28 = 1C (hex).
Description: Decimal: (1 × 2⁴) + (1 × 2³) + (1 × 2²) = 16 + 8 + 4 = 28. Hex: 28 ÷ 16 = 1 remainder 12 (C).
Description: Decimal: (1 × 2⁴) + (1 × 2³) + (1 × 2²) = 16 + 8 + 4 = 28. Hex: 28 ÷ 16 = 1 remainder 12 (C).
5.
Answer: Octal 75 = 111101 (binary), decimal 61.
Description: 7 = 111, 5 = 101, so 75 = 111101. Decimal: (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 61.
Description: 7 = 111, 5 = 101, so 75 = 111101. Decimal: (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 61.
Ruwan Suraweera Changed status to publish