Worksheet for practicing conversions between octal, decimal, hexadecimal, and binary number systems.

Let's solve each of the problems step by step, converting between number systems (binary, octal, decimal, and hexadecimal).

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(1) 11 in octal is equal to ___ in decimal and ___ in hexadecimal

- Octal: `11₈`
→ $ 1 \times 8^1 + 1 \times 8^0 = 8 + 1 = 9_{10} $
- Decimal: `9₁₀`
- Convert 9 to hex: `9₁₆`

✔ Answer: 9 in decimal, 9 in hexadecimal

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(2) A in hexadecimal is equal to ___ in binary and ___ in decimal

- Hex: `A₁₆` = 10₁₀
- Binary: 10₁₀ = `1010₂`

✔ Answer: 1010 in binary, 10 in decimal

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(3) 23 in hexadecimal is equal to ___ in decimal and ___ in octal

- Hex: `23₁₆` = $ 2 \times 16 + 3 = 32 + 3 = 35_{10} $
- Convert 35 to octal:
- $ 35 \div 8 = 4 $ remainder 3
- So, `43₈`

✔ Answer: 35 in decimal, 43 in octal

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(4) 31 in hexadecimal is equal to ___ in octal and ___ in binary

- Hex: `31₁₆` = $ 3 \times 16 + 1 = 48 + 1 = 49_{10} $
- Convert 49 to octal:
- $ 49 \div 8 = 6 $ rem 1 → `61₈`
- Convert 49 to binary:
- $ 49 = 32 + 16 + 1 = 110001₂ $

✔ Answer: 61 in octal, 110001 in binary

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(5) 63 in hexadecimal is equal to ___ in binary

- Hex: `63₁₆` = $ 6 \times 16 + 3 = 96 + 3 = 99_{10} $
- Convert 99 to binary:
- $ 64 + 32 + 2 + 1 = 1100011₂ $

✔ Answer: 1100011 in binary

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(6) 327 in octal is equal to ___ in binary and ___ in hexadecimal

- Octal: `327₈`
- Convert to decimal:
- $ 3 \times 8^2 + 2 \times 8^1 + 7 \times 8^0 = 3 \times 64 + 2 \times 8 + 7 = 192 + 16 + 7 = 215_{10} $
- Convert 215 to binary:
- $ 128 + 64 + 16 + 4 + 2 + 1 = 11010111₂ $
- Convert 215 to hex:
- $ 215 \div 16 = 13 $ rem 7 → `D7₁₆` (since 13 = D)

✔ Answer: 11010111 in binary, D7 in hexadecimal

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(7) 731 in octal is equal to ___ in decimal

- Octal: `731₈`
- $ 7 \times 8^2 + 3 \times 8^1 + 1 \times 8^0 = 7 \times 64 + 3 \times 8 + 1 = 448 + 24 + 1 = 473_{10} $

✔ Answer: 473 in decimal

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(8) 1021 in octal is equal to ___ in hexadecimal

- Octal: `1021₈`
- Convert to decimal:
- $ 1 \times 8^3 + 0 \times 8^2 + 2 \times 8^1 + 1 \times 8^0 = 512 + 0 + 16 + 1 = 529_{10} $
- Convert 529 to hex:
- $ 529 \div 16 = 33 $ rem 1
- $ 33 \div 16 = 2 $ rem 1
- So, `211₁₆`

✔ Answer: 211 in hexadecimal

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(9) 2F2 in hexadecimal is equal to ___ in binary

- Hex: `2F2₁₆`
- Each hex digit → 4 bits:
- 2 = 0010
- F = 1111
- 2 = 0010
- Combine: `0010 1111 0010` → `1011110010₂`

✔ Answer: 1011110010 in binary

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(10) 962 in decimal is equal to ___ in hexadecimal and ___ in octal

- Decimal: 962
- To hex:
- $ 962 \div 16 = 60 $ rem 2
- $ 60 \div 16 = 3 $ rem 12 → C
- So, `3C2₁₆`
- To octal:
- $ 962 \div 8 = 120 $ rem 2
- $ 120 \div 8 = 15 $ rem 0
- $ 15 \div 8 = 1 $ rem 7
- $ 1 \div 8 = 0 $ rem 1
- So, `1702₈`

✔ Answer: 3C2 in hexadecimal, 1702 in octal

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(11) 3 in decimal is equal to ___ in octal

- $ 3 \div 8 = 0 $ rem 3 → `3₈`

✔ Answer: 3 in octal

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(12) 42 in octal is equal to ___ in hexadecimal

- Octal: `42₈` = $ 4 \times 8 + 2 = 32 + 2 = 34_{10} $
- Convert 34 to hex:
- $ 34 \div 16 = 2 $ rem 2 → `22₁₆`

✔ Answer: 22 in hexadecimal

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(13) 92 in decimal is equal to ___ in octal

- $ 92 \div 8 = 11 $ rem 4
- $ 11 \div 8 = 1 $ rem 3
- $ 1 \div 8 = 0 $ rem 1
- So, `134₈`

✔ Answer: 134 in octal

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(14) 10001111 in binary is equal to ___ in hexadecimal and ___ in decimal

- Binary: `10001111₂`
- Group into 4s from right: `1000 1111`
- 1000 = 8, 1111 = F → `8F₁₆`
- Decimal: $ 128 + 0 + 0 + 0 + 8 + 4 + 2 + 1 = 143_{10} $

✔ Answer: 8F in hexadecimal, 143 in decimal

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(15) A1 in hexadecimal is equal to ___ in binary

- A = 1010, 1 = 0001 → `10100001₂`

✔ Answer: 10100001 in binary

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(16) 130 in hexadecimal is equal to ___ in octal and ___ in decimal

- Hex: `130₁₆` = $ 1 \times 256 + 3 \times 16 + 0 = 256 + 48 = 304_{10} $
- Convert 304 to octal:
- $ 304 \div 8 = 38 $ rem 0
- $ 38 \div 8 = 4 $ rem 6
- $ 4 \div 8 = 0 $ rem 4
- So, `460₈`

✔ Answer: 460 in octal, 304 in decimal

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(17) 457 in decimal is equal to ___ in binary

- Divide by 2:
- 457 ÷ 2 = 228 r1
- 228 ÷ 2 = 114 r0
- 114 ÷ 2 = 57 r0
- 57 ÷ 2 = 28 r1
- 28 ÷ 2 = 14 r0
- 14 ÷ 2 = 7 r0
- 7 ÷ 2 = 3 r1
- 3 ÷ 2 = 1 r1
- 1 ÷ 2 = 0 r1
- Read up: `111000001₂`

✔ Answer: 111000001 in binary

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(18) 476 in decimal is equal to ___ in hexadecimal

- $ 476 \div 16 = 29 $ rem 12 → C
- $ 29 \div 16 = 1 $ rem 13 → D
- $ 1 \div 16 = 0 $ rem 1
- So, `1DC₁₆`

✔ Answer: 1DC in hexadecimal

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(19) 1E9 in hexadecimal is equal to ___ in decimal and ___ in octal

- Hex: `1E9₁₆` = $ 1 \times 256 + 14 \times 16 + 9 = 256 + 224 + 9 = 489_{10} $
- Convert 489 to octal:
- $ 489 \div 8 = 61 $ rem 1
- $ 61 \div 8 = 7 $ rem 5
- $ 7 \div 8 = 0 $ rem 7
- So, `751₈`

✔ Answer: 489 in decimal, 751 in octal

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(20) 653 in decimal is equal to ___ in binary and ___ in octal

- Convert 653 to binary:
- 512 + 128 + 16 + 4 + 1 = 653
- So, `1010001101₂`
- Convert to octal:
- Group binary into 3s from right: `1 010 001 101`
- 1 = 1, 010 = 2, 001 = 1, 101 = 5 → `1215₈`

✔ Answer: 1010001101 in binary, 1215 in octal

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✔ Final Answers:

| # | Answer |
|---|--------|
| (1) | 9, 9 |
| (2) | 1010, 10 |
| (3) | 35, 43 |
| (4) | 61, 110001 |
| (5) | 1100011 |
| (6) | 11010111, D7 |
| (7) | 473 |
| (8) | 211 |
| (9) | 1011110010 |
| (10) | 3C2, 1702 |
| (11) | 3 |
| (12) | 22 |
| (13) | 134 |
| (14) | 8F, 143 |
| (15) | 10100001 |
| (16) | 460, 304 |
| (17) | 111000001 |
| (18) | 1DC |
| (19) | 489, 751 |
| (20) | 1010001101, 1215 |

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