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Number Systems

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Number Systems Worksheet

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Number Systems Worksheet

Twenty mixed conversion questions to work through on paper.

About This Worksheet

Work on paper. Show full working for each question, exactly as you would in an assignment. Check each answer by converting it back to decimal. If you get one wrong, find which step went wrong before moving on.

Tip

Base, method, check — every time

Every answer should include the base, the method you used and a check. For example: 60₁₀ = 111100₂ (repeated division; check: 32 + 16 + 8 + 4 = 60 ✓).

Section A — To Decimal

Practice

Convert to decimal

Try each one on paper.

1.
$110110₂$
2.
$10000001₂$
3.
$11110000₂$
4.
$563₈$
5.
$7C₁₆$
6.
$1F4₁₆$

Section B — From Decimal

Practice

Convert from decimal

Try each one on paper.

1.
$60₁₀ to binary$
2.
$99₁₀ to binary$
3.
$99₁₀ to octal$
4.
$500₁₀ to hexadecimal$
5.
$4095₁₀ to hexadecimal$

Section C — Binary, Octal and Hex

Practice

Convert using grouping

Try each one on paper.

1.
$101011100₂ to octal and hex$
2.
$1000000001₂ to octal and hex$
3.
$4C2₁₆ to binary$
4.
$90B₁₆ to binary$
5.
$617₈ to binary$

Section D — Mixed and Applied

Practice

Mixed questions

Try each one on paper.

1.
$617₈ to hexadecimal$
2.
$1234₈ to hexadecimal$
3.
$Which colour code has red 0, green 128, blue 128?$
4.
$How many bits are needed to store 1000₁₀, and why?$

Take this with you

Before you go on

$Place value \to decimal; repeated division \leftarrow decimal; grouping (3s and 4s) between binary, octal and hex.$
$Base, method, check — every time.$

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