Free practice on Number Bases for Class 6, 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.
In base 10, each place is worth 10 times more moving left. 4321 = 4 thousands + 3 hundreds + 2 tens + 1 unit. Each digit is between 0 and 9.
| Place | Value |
|---|---|
| Units | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten thousands | 10,000 |
In base 2, each place doubles: 1, 2, 4, 8, 16, 32, 64… Only digits 0 and 1 are used. 1011₂ = 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11.
| Binary | Base 10 |
|---|---|
| 1 | 1 |
| 10 | 2 |
| 100 | 4 |
| 1000 | 8 |
| 1011 | 11 |
| 10000 | 16 |
Method: repeatedly divide by 2 and note the remainders. Read the remainders BOTTOM-UP. 13 ÷ 2 = 6 r 1. 6 ÷ 2 = 3 r 0. 3 ÷ 2 = 1 r 1. 1 ÷ 2 = 0 r 1. Read up: 1101₂.
Convert 110 (base 2) to base ten.
Write your answer, then check below.
Answer: 6
1×4 + 1×2 + 0×1 = 6.
Convert 1111 (base 2) to base ten.
Write your answer, then check below.
Answer: 15
8 + 4 + 2 + 1 = 15.
Convert 21 (base 5) to base ten.
Write your answer, then check below.
Answer: 11
2×5 + 1×1 = 11.
Convert 9 (base ten) to base 2.
Answer: A. 1001
9 = 8 + 1 = 1001 in base 2.
Convert 17 (base ten) to base 5.
Answer: B. 32 (base 5)
17 = 3 fives + 2 units = 32 in base 5.
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