10 questions · Form 4 Mathematics Bab 2: Number Bases
What is the place value of digit 4 in the number 2431₆?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. What is the place value of digit 4 in the number 2431₆?
Answer: A
Counting place values from right to left starting at 6⁰: digit 1 is 6⁰, digit 3 is 6¹, and digit 4 is at 6².
2. 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.
3. Convert 405₉ into Base 10.
Answer: A
405₉ = (4 × 9²) + (0 × 9¹) + (5 × 9⁰) = (4 × 81) + 0 + 5 = 324 + 5 = 329₁₀.
4. Calculate 1101₂ + 1011₂ in Base 2.
Answer: A
1101₂ (13₁₀) + 1011₂ (11₁₀) = 24₁₀. Converting 24₁₀ to binary: 24 = 16 + 8 = 11000₂.
5. 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.
6. 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.
7. Convert the octal number 57₈ to binary.
Answer: A
Convert each digit to 3-bit binary: 5₈ = 101₂, 7₈ = 111₂. Combining gives 101111₂.
8. 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.
9. 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.
10. If x₈ = 101110₂, find the value of x.
Answer: A
Group binary in threes from right: (101)(110)₂ = 56₈. Thus x = 56.