Free practice on Number Bases and Modulo Arithmetic for Class 5, following the Cameroon primary school curriculum (English subsystem). Every answer is explained, so a parent who is not sure of the answer can still help.
We count in base 10 — because we have 10 fingers. Each place is worth 10 times the one to its right. Base 2 (binary) uses only 0 and 1. Computers use base 2.
| Base 10 | Base 2 (binary) |
|---|---|
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 8 | 1000 |
| 10 | 1010 |
Each digit's place value doubles: 1, 2, 4, 8, 16, 32… Take 1101₂. It is 1×8 + 1×4 + 0×2 + 1×1 = 8+4+0+1 = 13 in base 10.
Modulo means REMAINDER after division. 17 mod 5 = 2, because 17 ÷ 5 = 3 remainder 2. Modulo is useful for cycles: clocks (mod 12), days (mod 7).
| Sum | Modulo |
|---|---|
| 17 ÷ 5 | remainder 2 → 17 mod 5 = 2 |
| 20 ÷ 6 | remainder 2 → 20 mod 6 = 2 |
| 23 ÷ 4 | remainder 3 → 23 mod 4 = 3 |
Convert 101 (base 2) to base ten.
Write your answer, then check below.
Answer: 5
1×4 + 0×2 + 1×1 = 5.
Convert 11 (base 2) to base ten.
Write your answer, then check below.
Answer: 3
1×2 + 1×1 = 3.
Convert 24 (base 5) to base ten.
Write your answer, then check below.
Answer: 14
2×5 + 4×1 = 14.
Convert 13 (base ten) to base 5.
Answer: A. 23 (base 5)
13 = 2 fives + 3 units = 23 in base 5.
Which digits can we use in base 2?
Answer: A. 0 and 1
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