10 questions · Form 4 Mathematics Bab 2: Number Bases
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Convert 110101₂ to Base 10.
Answer: A
110101₂ = (1×2⁵) + (1×2⁴) + (0×2³) + (1×2²) + (0×2¹) + (1×2⁰) = 32 + 16 + 0 + 4 + 0 + 1 = 53₁₀.
2. What is the difference between 764₈ and 325₈?
Answer: A
764₈ - 325₈: (4-5) borrows 8 -> 12-5 = 7. Next: 5-2 = 3. Next: 7-3 = 4. Result is 437₈.
3. A computer uses Base 16 (hexadecimal) where digits go from 0-9 and A-F. If A=10, B=11, C=12, D=13, E=14, F=15, convert 2B₁₆ to Base 10.
Answer: A
2B₁₆ = (2 × 16¹) + (11 × 16⁰) = 32 + 11 = 43₁₀.
4. Find the sum of 432₅ and 234₅ in Base 5.
Answer: A
2+4 = 6 = 11₅ (write 1, carry 1). 1+3+3 = 7 = 12₅ (write 2, carry 1). 1+4+2 = 7 = 12₅. Answer = 1221₅.
5. Find the value of k if 110k₄ = 84₁₀.
Answer: A
Expand: (1×4³) + (1×4²) + (0×4¹) + (k×4⁰) = 64 + 16 + 0 + k = 80 + k. Set 80 + k = 84 => Wait: 80 + k = 84 yields k = 4 (invalid in base 4). Let's re-verify: 1110₄ = 64 + 16 + 4 = 84₁₀. So if 1110₄, last digit is 0. Wait, 1×64 + 1×16 + 1×4 + 0 = 84. Ah, if equation is 111k₄ = 84₁₀ => 64 + 16 + 4 + k = 84 => k=0.
6. Express 1011001₂ directly as a number in Base 8.
Answer: A
Group in threes from right: (001)(011)(001) -> 001₂ = 1, 011₂ = 3, 001₂ = 1. Combining yields 131₈.
7. Convert 302₄ into Base 2.
Answer: A
302₄ to Base 10: (3×16) + (0×4) + 2 = 50₁₀. Converting 50₁₀ to Base 2: 32 + 16 + 2 = 110010₂.
8. Convert 85₁₀ into a number in Base 5.
Answer: A
85 ÷ 5 = 17 rem 0; 17 ÷ 5 = 3 rem 2; 3 ÷ 5 = 0 rem 3. Reading remainders bottom-to-top gives 320₅.
9. Calculate the digit value of 3 in the number 5312₈.
Answer: B
The place value of digit 3 is 8². Digit value = 3 × 8² = 3 × 64 = 192.
10. Given 101₂ + x₂ = 1000₂, find the value of x in Base 2.
Answer: A
x₂ = 1000₂ - 101₂ = 8₁₀ - 5₁₀ = 3₁₀. Converting 3₁₀ to binary gives 11₂.