Decimal to binary conversion worksheet with exercises for students to practice converting numbers between decimal and binary systems.

Let's solve each problem step by step.

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Part 1: Convert Decimal to Binary

We'll convert each decimal number to binary using repeated division by 2 (or by finding the largest power of 2 less than or equal to the number).

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#### 1) 145₁₀ → ?₂

Divide by 2 repeatedly:

- 145 ÷ 2 = 72 R 1
- 72 ÷ 2 = 36 R 0
- 36 ÷ 2 = 18 R 0
- 18 ÷ 2 = 9 R 0
- 9 ÷ 2 = 4 R 1
- 4 ÷ 2 = 2 R 0
- 2 ÷ 2 = 1 R 0
- 1 ÷ 2 = 0 R 1

Read remainders from bottom to top:
10010001₂

✔ Answer: 10010001₂

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#### 2) 124₁₀ → ?₂

- 124 ÷ 2 = 62 R 0
- 62 ÷ 2 = 31 R 0
- 31 ÷ 2 = 15 R 1
- 15 ÷ 2 = 7 R 1
- 7 ÷ 2 = 3 R 1
- 3 ÷ 2 = 1 R 1
- 1 ÷ 2 = 0 R 1

Remainders: 1111100₂

✔ Answer: 1111100₂

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#### 3) 242₁₀ → ?₂

- 242 ÷ 2 = 121 R 0
- 121 ÷ 2 = 60 R 1
- 60 ÷ 2 = 30 R 0
- 30 ÷ 2 = 15 R 0
- 15 ÷ 2 = 7 R 1
- 7 ÷ 2 = 3 R 1
- 3 ÷ 2 = 1 R 1
- 1 ÷ 2 = 0 R 1

Remainders: 11110010₂

✔ Answer: 11110010₂

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#### 4) 116₁₀ → ?₂

- 116 ÷ 2 = 58 R 0
- 58 ÷ 2 = 29 R 0
- 29 ÷ 2 = 14 R 1
- 14 ÷ 2 = 7 R 0
- 7 ÷ 2 = 3 R 1
- 3 ÷ 2 = 1 R 1
- 1 ÷ 2 = 0 R 1

Remainders: 1110100₂

✔ Answer: 1110100₂

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#### 5) 182₁₀ → ?₂

- 182 ÷ 2 = 91 R 0
- 91 ÷ 2 = 45 R 1
- 45 ÷ 2 = 22 R 1
- 22 ÷ 2 = 11 R 0
- 11 ÷ 2 = 5 R 1
- 5 ÷ 2 = 2 R 1
- 2 ÷ 2 = 1 R 0
- 1 ÷ 2 = 0 R 1

Remainders: 10111010₂

✔ Answer: 10111010₂

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#### 6) 70₁₀ → ?₂

- 70 ÷ 2 = 35 R 0
- 35 ÷ 2 = 17 R 1
- 17 ÷ 2 = 8 R 1
- 8 ÷ 2 = 4 R 0
- 4 ÷ 2 = 2 R 0
- 2 ÷ 2 = 1 R 0
- 1 ÷ 2 = 0 R 1

Remainders: 1000110₂

✔ Answer: 1000110₂

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#### 7) 238₁₀ → ?₂

- 238 ÷ 2 = 119 R 0
- 119 ÷ 2 = 59 R 1
- 59 ÷ 2 = 29 R 1
- 29 ÷ 2 = 14 R 1
- 14 ÷ 2 = 7 R 0
- 7 ÷ 2 = 3 R 1
- 3 ÷ 2 = 1 R 1
- 1 ÷ 2 = 0 R 1

Remainders: 11110110₂

✔ Answer: 11110110₂

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#### 8) 164₁₀ → ?₂

- 164 ÷ 2 = 82 R 0
- 82 ÷ 2 = 41 R 0
- 41 ÷ 2 = 20 R 1
- 20 ÷ 2 = 10 R 0
- 10 ÷ 2 = 5 R 0
- 5 ÷ 2 = 2 R 1
- 2 ÷ 2 = 1 R 0
- 1 ÷ 2 = 0 R 1

Remainders: 10101000₂

✔ Answer: 10101000₂

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Part 2: Convert Binary to Decimal

Use place values: powers of 2 from right to left (starting at 2⁰).

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#### 9) 10010110₂ → ?₁₀

Positions (from right):
`1 0 0 1 0 1 1 0`
→ 2⁷ 2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
= 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0 =
128 + 16 + 4 + 2 = 150

✔ Answer: 150₁₀

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#### 10) 10001011₂ → ?₁₀

Positions:
`1 0 0 0 1 0 1 1`
= 128 + 0 + 0 + 0 + 8 + 0 + 2 + 1 =
128 + 8 + 2 + 1 = 139

✔ Answer: 139₁₀

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#### 11) 1100111₂ → ?₁₀

`1 1 0 0 1 1 1`
= 64 + 32 + 0 + 0 + 4 + 2 + 1 =
64 + 32 + 4 + 2 + 1 = 103

✔ Answer: 103₁₀

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#### 12) 1100100₂ → ?₁₀

`1 1 0 0 1 0 0`
= 64 + 32 + 0 + 0 + 4 + 0 + 0 =
64 + 32 + 4 = 100

✔ Answer: 100₁₀

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#### 13) 1000000₂ → ?₁₀

Only the leftmost bit is 1:
= 2⁶ = 64

✔ Answer: 64₁₀

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#### 14) 11000101₂ → ?₁₀

`1 1 0 0 0 1 0 1`
= 128 + 64 + 0 + 0 + 0 + 4 + 0 + 1 =
128 + 64 + 4 + 1 = 197

✔ Answer: 197₁₀

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#### 15) 11010010₂ → ?₁₀

`1 1 0 1 0 0 1 0`
= 128 + 64 + 0 + 8 + 0 + 0 + 2 + 0 =
128 + 64 + 8 + 2 = 202

✔ Answer: 202₁₀

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#### 16) 1010100₂ → ?₁₀

`1 0 1 0 1 0 0`
= 64 + 0 + 16 + 0 + 4 + 0 + 0 =
64 + 16 + 4 = 84

✔ Answer: 84₁₀

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✔ Final Answers:

#### Decimal to Binary:
1) 145₁₀ = 10010001₂
2) 124₁₀ = 1111100₂
3) 242₁₀ = 11110010₂
4) 116₁₀ = 1110100₂
5) 182₁₀ = 10111010₂
6) 70₁₀ = 1000110₂
7) 238₁₀ = 11110110₂
8) 164₁₀ = 10101000₂

#### Binary to Decimal:
9) 10010110₂ = 150₁₀
10) 10001011₂ = 139₁₀
11) 1100111₂ = 103₁₀
12) 1100100₂ = 100₁₀
13) 1000000₂ = 64₁₀
14) 11000101₂ = 197₁₀
15) 11010010₂ = 202₁₀
16) 1010100₂ = 84₁₀

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