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Number Systems Worksheet Generator

Binary, decimal, hexadecimal and octal conversions, binary addition and two's complement. No AI, no credits.

Grades 6 – 12No account needed

Practice sheets for binary, decimal, hexadecimal and octal conversions, binary addition, 8-bit two's complement, and bits, bytes and storage units. States decimal versus binary prefixes. Every answer is computed by code. No AI, so it never uses a generation credit.

What students practice

  • Computer Science
  • Number systems
  • Binary

Live sample sheet

No account needed to view and print.
Name: ____________________Date: ____________

Number Systems

1. Convert 1110₂ to decimal.
2. Convert 43 to binary.
3. Convert 35 to hexadecimal.
4. Convert 1001₂ to decimal.
5. Convert 30 to binary.
6. Convert 43 to hexadecimal.
7. Convert 10011₂ to decimal.
8. Convert 8 to binary.
9. Convert 92 to hexadecimal.
10. Convert 111₂ to decimal.
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Answer Key — Number Systems

1. Convert 1110₂ to decimal.
Solution:
1 × 2^3 = 8
1 × 2^2 = 4
1 × 2^1 = 2
0 × 2^0 = 0
8 + 4 + 2 + 0 = 14
Answer: 14
2. Convert 43 to binary.
Solution:
43 ÷ 2 = 21 remainder 1 → 1
21 ÷ 2 = 10 remainder 1 → 1
10 ÷ 2 = 5 remainder 0 → 1
5 ÷ 2 = 2 remainder 1 → 1
2 ÷ 2 = 1 remainder 0 → 1
1 ÷ 2 = 0 remainder 1 → 1
Result: 101011₂
Answer: 101011₂
3. Convert 35 to hexadecimal.
Solution:
35 ÷ 16 = 2 remainder 3
Remainder 3 → 3
Quotient 2 → 2
Result: 23₁₆
Answer: 23₁₆
4. Convert 1001₂ to decimal.
Solution:
1 × 2^3 = 8
0 × 2^2 = 0
0 × 2^1 = 0
1 × 2^0 = 1
8 + 0 + 0 + 1 = 9
Answer: 9
5. Convert 30 to binary.
Solution:
30 ÷ 2 = 15 remainder 0 → 0
15 ÷ 2 = 7 remainder 1 → 0
7 ÷ 2 = 3 remainder 1 → 0
3 ÷ 2 = 1 remainder 1 → 0
1 ÷ 2 = 0 remainder 1 → 0
0 ÷ 2 = 0 remainder 0 → 0
Result: 11110₂
Answer: 11110₂
6. Convert 43 to hexadecimal.
Solution:
43 ÷ 16 = 2 remainder 11
Remainder 11 → B
Quotient 2 → 2
Result: 2B₁₆
Answer: 2B₁₆
7. Convert 10011₂ to decimal.
Solution:
1 × 2^4 = 16
0 × 2^3 = 0
0 × 2^2 = 0
1 × 2^1 = 2
1 × 2^0 = 1
16 + 0 + 0 + 2 + 1 = 19
Answer: 19
8. Convert 8 to binary.
Solution:
8 ÷ 2 = 4 remainder 0 → 1
4 ÷ 2 = 2 remainder 0 → 1
2 ÷ 2 = 1 remainder 0 → 1
1 ÷ 2 = 0 remainder 1 → 1
Result: 1000₂
Answer: 1000₂
9. Convert 92 to hexadecimal.
Solution:
92 ÷ 16 = 5 remainder 12
Remainder 12 → C
Quotient 5 → 5
Result: 5C₁₆
Answer: 5C₁₆
10. Convert 111₂ to decimal.
Solution:
1 × 2^2 = 4
1 × 2^1 = 2
1 × 2^0 = 1
4 + 2 + 1 = 7
Answer: 7
Answers computed by code. No AI, no credits.

Assumptions and Conventions

Assumptions:
  • Binary uses base 2, octal uses base 8, decimal uses base 10, hexadecimal uses base 16.
  • 8-bit two's complement range: -128 to 127.
  • Decimal prefixes: KB = 1000 bytes, MB = 1,000,000 bytes.
  • Binary prefixes: KiB = 1024 bytes, MiB = 1,048,576 bytes.
Conventions:
  • Subscript notation: ₂ for binary, ₈ for octal, ₁₀ for decimal, ₁₆ for hexadecimal.
  • Storage unit conversions state whether the prefix is decimal (KB, MB) or binary (KiB, MiB).
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Frequently asked questions

Do students need an account to use the Number Systems?

No. Students never need an account. They open a shared link or join with a code.

Can I print the Number Systems without signing up?

Yes. This tool computes answers by code, so you can generate, preview and print worksheet without an account. A free account adds saving and student links.

How are the answers computed?

Every answer is computed by code and verified by a second independent method. No AI is used.

What grades is the Number Systems for?

This tool fits Grades 6 – 12.

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Sample output, computed by code — change the options and Generate to make your own
Name: ____________________Date: ____________

Number Systems

1. Convert 10011₂ to decimal.
2. Convert 26 to binary.
3. Convert 49₁₆ to decimal.
4. Convert 1100₂ to decimal.
5. Convert 52 to binary.
6. Convert 67 to hexadecimal.
7. Convert 111110₂ to decimal.
8. Convert 8 to binary.
9. Convert 45₁₆ to decimal.
10. Convert 110111₂ to decimal.
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Answer Key — Number Systems

1. Convert 10011₂ to decimal.
Solution:
1 × 2^4 = 16
0 × 2^3 = 0
0 × 2^2 = 0
1 × 2^1 = 2
1 × 2^0 = 1
16 + 0 + 0 + 2 + 1 = 19
Answer: 19
2. Convert 26 to binary.
Solution:
26 ÷ 2 = 13 remainder 0 → 1
13 ÷ 2 = 6 remainder 1 → 1
6 ÷ 2 = 3 remainder 0 → 1
3 ÷ 2 = 1 remainder 1 → 1
1 ÷ 2 = 0 remainder 1 → 1
Result: 11010₂
Answer: 11010₂
3. Convert 49₁₆ to decimal.
Solution:
4 × 16^1 = 64
9 × 16^0 = 9
64 + 9 = 73
Answer: 73
4. Convert 1100₂ to decimal.
Solution:
1 × 2^3 = 8
1 × 2^2 = 4
0 × 2^1 = 0
0 × 2^0 = 0
8 + 4 + 0 + 0 = 12
Answer: 12
5. Convert 52 to binary.
Solution:
52 ÷ 2 = 26 remainder 0 → 1
26 ÷ 2 = 13 remainder 0 → 1
13 ÷ 2 = 6 remainder 1 → 1
6 ÷ 2 = 3 remainder 0 → 1
3 ÷ 2 = 1 remainder 1 → 1
1 ÷ 2 = 0 remainder 1 → 1
Result: 110100₂
Answer: 110100₂
6. Convert 67 to hexadecimal.
Solution:
67 ÷ 16 = 4 remainder 3
Remainder 3 → 3
Quotient 4 → 4
Result: 43₁₆
Answer: 43₁₆
7. Convert 111110₂ to decimal.
Solution:
1 × 2^5 = 32
1 × 2^4 = 16
1 × 2^3 = 8
1 × 2^2 = 4
1 × 2^1 = 2
0 × 2^0 = 0
32 + 16 + 8 + 4 + 2 + 0 = 62
Answer: 62
8. Convert 8 to binary.
Solution:
8 ÷ 2 = 4 remainder 0 → 0
4 ÷ 2 = 2 remainder 0 → 0
2 ÷ 2 = 1 remainder 0 → 0
1 ÷ 2 = 0 remainder 1 → 0
0 ÷ 2 = 0 remainder 0 → 0
Result: 1000₂
Answer: 1000₂
9. Convert 45₁₆ to decimal.
Solution:
4 × 16^1 = 64
5 × 16^0 = 5
64 + 5 = 69
Answer: 69
10. Convert 110111₂ to decimal.
Solution:
1 × 2^5 = 32
1 × 2^4 = 16
0 × 2^3 = 0
1 × 2^2 = 4
1 × 2^1 = 2
1 × 2^0 = 1
32 + 16 + 0 + 4 + 2 + 1 = 55
Answer: 55
Answers computed by code. No AI, no credits.

Assumptions and Conventions

Assumptions:
  • Binary uses base 2, octal uses base 8, decimal uses base 10, hexadecimal uses base 16.
  • 8-bit two's complement range: -128 to 127.
  • Decimal prefixes: KB = 1000 bytes, MB = 1,000,000 bytes.
  • Binary prefixes: KiB = 1024 bytes, MiB = 1,048,576 bytes.
Conventions:
  • Subscript notation: ₂ for binary, ₈ for octal, ₁₀ for decimal, ₁₆ for hexadecimal.
  • Storage unit conversions state whether the prefix is decimal (KB, MB) or binary (KiB, MiB).
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Number Systems - High school CS - Conversions and arithmetic

Binary, decimal, hexadecimal and octal conversions, binary arithmetic, and storage units. No AI, no credits.

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