Decimal to Binary Conversion Worksheet with practice problems and scratch area.
Worksheet for converting decimal numbers to binary, showing examples and practice problems with 8-bit binary representation.
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Show Answer Key & Explanations
Step-by-step solution for: Decimal to Binary Conversion worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Decimal to Binary Conversion worksheet
To convert decimal numbers to binary using 8 bits, we use the place values: 128, 64, 32, 16, 8, 4, 2, 1.
For each number, we check if it can be subtracted by each of these values (starting from 128 down to 1). If yes, we write a “1” in that position and subtract. If no, we write a “0”.
Let’s go step by step for each number on the worksheet:
---
1. 238
- 238 ≥ 128 → 1, remainder = 238 - 128 = 110
- 110 ≥ 64 → 1, remainder = 110 - 64 = 46
- 46 ≥ 32 → 1, remainder = 46 - 32 = 14
- 14 < 16 → 0
- 14 ≥ 8 → 1, remainder = 14 - 8 = 6
- 6 ≥ 4 → 1, remainder = 6 - 4 = 2
- 2 ≥ 2 → 1, remainder = 2 - 2 = 0
- 0 < 1 → 0
→ Binary: 11101110
*(This matches the example already filled in the worksheet — good!)*
---
2. 34
- 34 < 128 → 0
- 34 < 64 → 0
- 34 ≥ 32 → 1, remainder = 34 - 32 = 2
- 2 < 16 → 0
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, remainder = 0
- 0 < 1 → 0
→ Binary: 00100010
*(Also matches the example — perfect!)*
---
Now let’s do the rest:
---
3. 123
- 123 < 128 → 0
- 123 ≥ 64 → 1, rem = 59
- 59 ≥ 32 → 1, rem = 27
- 27 ≥ 16 → 1, rem = 11
- 11 ≥ 8 → 1, rem = 3
- 3 < 4 → 0
- 3 ≥ 2 → 1, rem = 1
- 1 ≥ 1 → 1, rem = 0
→ 01111011
---
4. 50
- 50 < 128 → 0
- 50 < 64 → 0
- 50 ≥ 32 → 1, rem = 18
- 18 ≥ 16 → 1, rem = 2
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 00110010
---
5. 255
All bits set to 1 because 255 is max for 8 bits.
→ 11111111
---
6. 200
- 200 ≥ 128 → 1, rem = 72
- 72 ≥ 64 → 1, rem = 8
- 8 < 32 → 0
- 8 < 16 → 0
- 8 ≥ 8 → 1, rem = 0
- 0 < 4 → 0
- 0 < 2 → 0
- 0 < 1 → 0
→ 11001000
---
7. 10
- 10 < 128 → 0
- 10 < 64 → 0
- 10 < 32 → 0
- 10 < 16 → 0
- 10 ≥ 8 → 1, rem = 2
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 00001010
---
8. 138
- 138 ≥ 128 → 1, rem = 10
- 10 < 64 → 0
- 10 < 32 → 0
- 10 < 16 → 0
- 10 ≥ 8 → 1, rem = 2
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 10001010
---
9. 1
Only last bit:
→ 00000001
---
10. 13
- 13 < 128 → 0
- 13 < 64 → 0
- 13 < 32 → 0
- 13 < 16 → 0
- 13 ≥ 8 → 1, rem = 5
- 5 ≥ 4 → 1, rem = 1
- 1 < 2 → 0
- 1 ≥ 1 → 1, rem = 0
→ 00001101
---
11. 250
- 250 ≥ 128 → 1, rem = 122
- 122 ≥ 64 → 1, rem = 58
- 58 ≥ 32 → 1, rem = 26
- 26 ≥ 16 → 1, rem = 10
- 10 ≥ 8 → 1, rem = 2
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 11111010
---
12. 107
- 107 < 128 → 0
- 107 ≥ 64 → 1, rem = 43
- 43 ≥ 32 → 1, rem = 11
- 11 < 16 → 0
- 11 ≥ 8 → 1, rem = 3
- 3 < 4 → 0
- 3 ≥ 2 → 1, rem = 1
- 1 ≥ 1 → 1, rem = 0
→ 01101011
---
13. 224
- 224 ≥ 128 → 1, rem = 96
- 96 ≥ 64 → 1, rem = 32
- 32 ≥ 32 → 1, rem = 0
- Rest are 0
→ 11100000
---
14. 114
- 114 < 128 → 0
- 114 ≥ 64 → 1, rem = 50
- 50 ≥ 32 → 1, rem = 18
- 18 ≥ 16 → 1, rem = 2
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 01110010
---
15. 192
- 192 ≥ 128 → 1, rem = 64
- 64 ≥ 64 → 1, rem = 0
- Rest 0
→ 11000000
---
16. 172
- 172 ≥ 128 → 1, rem = 44
- 44 < 64 → 0
- 44 ≥ 32 → 1, rem = 12
- 12 < 16 → 0
- 12 ≥ 8 → 1, rem = 4
- 4 ≥ 4 → 1, rem = 0
- 0 < 2 → 0
- 0 < 1 → 0
→ 10101100
---
17. 100
- 100 < 128 → 0
- 100 ≥ 64 → 1, rem = 36
- 36 ≥ 32 → 1, rem = 4
- 4 < 16 → 0
- 4 < 8 → 0
- 4 ≥ 4 → 1, rem = 0
- 0 < 2 → 0
- 0 < 1 → 0
→ 01100100
---
18. 119
- 119 < 128 → 0
- 119 ≥ 64 → 1, rem = 55
- 55 ≥ 32 → 1, rem = 23
- 23 ≥ 16 → 1, rem = 7
- 7 < 8 → 0? Wait — 7 < 8 → 0? No, 7 < 8 → so 0? Actually 7 < 8 → yes → 0
Wait — correction:
Actually:
After 23 - 16 = 7
7 < 8 → 0
7 ≥ 4 → 1, rem = 3
3 ≥ 2 → 1, rem = 1
1 ≥ 1 → 1, rem = 0
So:
→ 01110111
Check: 64+32+16+4+2+1 = 119 → correct.
---
19. 57
- 57 < 128 → 0
- 57 < 64 → 0
- 57 ≥ 32 → 1, rem = 25
- 25 ≥ 16 → 1, rem = 9
- 9 ≥ 8 → 1, rem = 1
- 1 < 4 → 0
- 1 < 2 → 0
- 1 ≥ 1 → 1, rem = 0
→ 00111001
---
20. 98
- 98 < 128 → 0
- 98 ≥ 64 → 1, rem = 34
- 34 ≥ 32 → 1, rem = 2
- 2 < 16 → 0
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 01100010
---
21. 179
- 179 ≥ 128 → 1, rem = 51
- 51 < 64 → 0
- 51 ≥ 32 → 1, rem = 19
- 19 ≥ 16 → 1, rem = 3
- 3 < 8 → 0
- 3 < 4 → 0
- 3 ≥ 2 → 1, rem = 1
- 1 ≥ 1 → 1, rem = 0
→ 10110011
---
22. 2
Only the '2' bit:
→ 00000010
---
Final Answer:
11101110
00100010
01111011
00110010
11111111
11001000
00001010
10001010
00000001
00001101
11111010
01101011
11100000
01110010
11000000
10101100
01100100
01110111
00111001
01100010
10110011
00000010
For each number, we check if it can be subtracted by each of these values (starting from 128 down to 1). If yes, we write a “1” in that position and subtract. If no, we write a “0”.
Let’s go step by step for each number on the worksheet:
---
1. 238
- 238 ≥ 128 → 1, remainder = 238 - 128 = 110
- 110 ≥ 64 → 1, remainder = 110 - 64 = 46
- 46 ≥ 32 → 1, remainder = 46 - 32 = 14
- 14 < 16 → 0
- 14 ≥ 8 → 1, remainder = 14 - 8 = 6
- 6 ≥ 4 → 1, remainder = 6 - 4 = 2
- 2 ≥ 2 → 1, remainder = 2 - 2 = 0
- 0 < 1 → 0
→ Binary: 11101110
*(This matches the example already filled in the worksheet — good!)*
---
2. 34
- 34 < 128 → 0
- 34 < 64 → 0
- 34 ≥ 32 → 1, remainder = 34 - 32 = 2
- 2 < 16 → 0
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, remainder = 0
- 0 < 1 → 0
→ Binary: 00100010
*(Also matches the example — perfect!)*
---
Now let’s do the rest:
---
3. 123
- 123 < 128 → 0
- 123 ≥ 64 → 1, rem = 59
- 59 ≥ 32 → 1, rem = 27
- 27 ≥ 16 → 1, rem = 11
- 11 ≥ 8 → 1, rem = 3
- 3 < 4 → 0
- 3 ≥ 2 → 1, rem = 1
- 1 ≥ 1 → 1, rem = 0
→ 01111011
---
4. 50
- 50 < 128 → 0
- 50 < 64 → 0
- 50 ≥ 32 → 1, rem = 18
- 18 ≥ 16 → 1, rem = 2
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 00110010
---
5. 255
All bits set to 1 because 255 is max for 8 bits.
→ 11111111
---
6. 200
- 200 ≥ 128 → 1, rem = 72
- 72 ≥ 64 → 1, rem = 8
- 8 < 32 → 0
- 8 < 16 → 0
- 8 ≥ 8 → 1, rem = 0
- 0 < 4 → 0
- 0 < 2 → 0
- 0 < 1 → 0
→ 11001000
---
7. 10
- 10 < 128 → 0
- 10 < 64 → 0
- 10 < 32 → 0
- 10 < 16 → 0
- 10 ≥ 8 → 1, rem = 2
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 00001010
---
8. 138
- 138 ≥ 128 → 1, rem = 10
- 10 < 64 → 0
- 10 < 32 → 0
- 10 < 16 → 0
- 10 ≥ 8 → 1, rem = 2
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 10001010
---
9. 1
Only last bit:
→ 00000001
---
10. 13
- 13 < 128 → 0
- 13 < 64 → 0
- 13 < 32 → 0
- 13 < 16 → 0
- 13 ≥ 8 → 1, rem = 5
- 5 ≥ 4 → 1, rem = 1
- 1 < 2 → 0
- 1 ≥ 1 → 1, rem = 0
→ 00001101
---
11. 250
- 250 ≥ 128 → 1, rem = 122
- 122 ≥ 64 → 1, rem = 58
- 58 ≥ 32 → 1, rem = 26
- 26 ≥ 16 → 1, rem = 10
- 10 ≥ 8 → 1, rem = 2
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 11111010
---
12. 107
- 107 < 128 → 0
- 107 ≥ 64 → 1, rem = 43
- 43 ≥ 32 → 1, rem = 11
- 11 < 16 → 0
- 11 ≥ 8 → 1, rem = 3
- 3 < 4 → 0
- 3 ≥ 2 → 1, rem = 1
- 1 ≥ 1 → 1, rem = 0
→ 01101011
---
13. 224
- 224 ≥ 128 → 1, rem = 96
- 96 ≥ 64 → 1, rem = 32
- 32 ≥ 32 → 1, rem = 0
- Rest are 0
→ 11100000
---
14. 114
- 114 < 128 → 0
- 114 ≥ 64 → 1, rem = 50
- 50 ≥ 32 → 1, rem = 18
- 18 ≥ 16 → 1, rem = 2
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 01110010
---
15. 192
- 192 ≥ 128 → 1, rem = 64
- 64 ≥ 64 → 1, rem = 0
- Rest 0
→ 11000000
---
16. 172
- 172 ≥ 128 → 1, rem = 44
- 44 < 64 → 0
- 44 ≥ 32 → 1, rem = 12
- 12 < 16 → 0
- 12 ≥ 8 → 1, rem = 4
- 4 ≥ 4 → 1, rem = 0
- 0 < 2 → 0
- 0 < 1 → 0
→ 10101100
---
17. 100
- 100 < 128 → 0
- 100 ≥ 64 → 1, rem = 36
- 36 ≥ 32 → 1, rem = 4
- 4 < 16 → 0
- 4 < 8 → 0
- 4 ≥ 4 → 1, rem = 0
- 0 < 2 → 0
- 0 < 1 → 0
→ 01100100
---
18. 119
- 119 < 128 → 0
- 119 ≥ 64 → 1, rem = 55
- 55 ≥ 32 → 1, rem = 23
- 23 ≥ 16 → 1, rem = 7
- 7 < 8 → 0? Wait — 7 < 8 → 0? No, 7 < 8 → so 0? Actually 7 < 8 → yes → 0
Wait — correction:
Actually:
After 23 - 16 = 7
7 < 8 → 0
7 ≥ 4 → 1, rem = 3
3 ≥ 2 → 1, rem = 1
1 ≥ 1 → 1, rem = 0
So:
→ 01110111
Check: 64+32+16+4+2+1 = 119 → correct.
---
19. 57
- 57 < 128 → 0
- 57 < 64 → 0
- 57 ≥ 32 → 1, rem = 25
- 25 ≥ 16 → 1, rem = 9
- 9 ≥ 8 → 1, rem = 1
- 1 < 4 → 0
- 1 < 2 → 0
- 1 ≥ 1 → 1, rem = 0
→ 00111001
---
20. 98
- 98 < 128 → 0
- 98 ≥ 64 → 1, rem = 34
- 34 ≥ 32 → 1, rem = 2
- 2 < 16 → 0
- 2 < 8 → 0
- 2 < 4 → 0
- 2 ≥ 2 → 1, rem = 0
- 0 < 1 → 0
→ 01100010
---
21. 179
- 179 ≥ 128 → 1, rem = 51
- 51 < 64 → 0
- 51 ≥ 32 → 1, rem = 19
- 19 ≥ 16 → 1, rem = 3
- 3 < 8 → 0
- 3 < 4 → 0
- 3 ≥ 2 → 1, rem = 1
- 1 ≥ 1 → 1, rem = 0
→ 10110011
---
22. 2
Only the '2' bit:
→ 00000010
---
Final Answer:
11101110
00100010
01111011
00110010
11111111
11001000
00001010
10001010
00000001
00001101
11111010
01101011
11100000
01110010
11000000
10101100
01100100
01110111
00111001
01100010
10110011
00000010
Parent Tip: Review the logic above to help your child master the concept of decimal to binary worksheet.
