Convert decimal to binary and binary to decimal with this math worksheet.
Worksheet for converting decimal and binary numbers with problems and blank spaces for answers.
PNG
612×792
5.9 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #659020
⭐
Show Answer Key & Explanations
Step-by-step solution for: Number Systems Worksheets | Dynamically Created Number Systems ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Number Systems Worksheets | Dynamically Created Number Systems ...
Problem: Converting Decimal and Binary Numbers
The task involves two parts:
1. Converting Decimal numbers to Binary equivalents.
2. Converting Binary numbers to Decimal equivalents.
Let's solve each part step by step.
---
Part 1: Converting Decimal to Binary
#### Step-by-Step Method for Decimal to Binary Conversion:
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. The binary equivalent is obtained by reading the remainders in reverse order (from bottom to top).
#### Solutions:
1. 145<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 145 by 2:
145 ÷ 2 = 72 remainder 1
72 ÷ 2 = 36 remainder 0
36 ÷ 2 = 18 remainder 0
18 ÷ 2 = 9 remainder 0
9 ÷ 2 = 4 remainder 1
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 10010001
- Answer: 145<sub>(10)</sub> = 10010001<sub>(2)</sub>
2. 124<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 124 by 2:
124 ÷ 2 = 62 remainder 0
62 ÷ 2 = 31 remainder 0
31 ÷ 2 = 15 remainder 1
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 1111100
- Answer: 124<sub>(10)</sub> = 1111100<sub>(2)</sub>
3. 242<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 242 by 2:
242 ÷ 2 = 121 remainder 0
121 ÷ 2 = 60 remainder 1
60 ÷ 2 = 30 remainder 0
30 ÷ 2 = 15 remainder 0
15 ÷ 2 = 7 remainder 1
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 11110010
- Answer: 242<sub>(10)</sub> = 11110010<sub>(2)</sub>
4. 116<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 116 by 2:
116 ÷ 2 = 58 remainder 0
58 ÷ 2 = 29 remainder 0
29 ÷ 2 = 14 remainder 1
14 ÷ 2 = 7 remainder 0
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 1110100
- Answer: 116<sub>(10)</sub> = 1110100<sub>(2)</sub>
5. 182<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 182 by 2:
182 ÷ 2 = 91 remainder 0
91 ÷ 2 = 45 remainder 1
45 ÷ 2 = 22 remainder 1
22 ÷ 2 = 11 remainder 0
11 ÷ 2 = 5 remainder 1
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 10110110
- Answer: 182<sub>(10)</sub> = 10110110<sub>(2)</sub>
6. 70<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 70 by 2:
70 ÷ 2 = 35 remainder 0
35 ÷ 2 = 17 remainder 1
17 ÷ 2 = 8 remainder 1
8 ÷ 2 = 4 remainder 0
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 1000110
- Answer: 70<sub>(10)</sub> = 1000110<sub>(2)</sub>
7. 238<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 238 by 2:
238 ÷ 2 = 119 remainder 0
119 ÷ 2 = 59 remainder 1
59 ÷ 2 = 29 remainder 1
29 ÷ 2 = 14 remainder 1
14 ÷ 2 = 7 remainder 0
7 ÷ 2 = 3 remainder 1
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 11101110
- Answer: 238<sub>(10)</sub> = 11101110<sub>(2)</sub>
8. 164<sub>(10)</sub> = ?<sub>(2)</sub>
- Divide 164 by 2:
164 ÷ 2 = 82 remainder 0
82 ÷ 2 = 41 remainder 0
41 ÷ 2 = 20 remainder 1
20 ÷ 2 = 10 remainder 0
10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
- Reading the remainders from bottom to top: 10100100
- Answer: 164<sub>(10)</sub> = 10100100<sub>(2)</sub>
---
Part 2: Converting Binary to Decimal
#### Step-by-Step Method for Binary to Decimal Conversion:
To convert a binary number to decimal, multiply each digit by \(2^n\), where \(n\) is the position of the digit from right to left (starting at 0), and sum the results.
#### Solutions:
9. 10010110<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 10010110
- Positions: \(2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^7 + 0 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0\)
\(= 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0\)
\(= 150\)
- Answer: 10010110<sub>(2)</sub> = 150<sub>(10)</sub>
10. 10001011<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 10001011
- Positions: \(2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^7 + 0 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
\(= 128 + 0 + 0 + 0 + 8 + 0 + 2 + 1\)
\(= 139\)
- Answer: 10001011<sub>(2)</sub> = 139<sub>(10)</sub>
11. 1100111<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 1100111
- Positions: \(2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)
\(= 64 + 32 + 0 + 0 + 4 + 2 + 1\)
\(= 103\)
- Answer: 1100111<sub>(2)</sub> = 103<sub>(10)</sub>
12. 1100100<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 1100100
- Positions: \(2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0\)
\(= 64 + 32 + 0 + 0 + 4 + 0 + 0\)
\(= 100\)
- Answer: 1100100<sub>(2)</sub> = 100<sub>(10)</sub>
13. 1000000<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 1000000
- Positions: \(2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 0 \times 2^0\)
\(= 64 + 0 + 0 + 0 + 0 + 0 + 0\)
\(= 64\)
- Answer: 1000000<sub>(2)</sub> = 64<sub>(10)</sub>
14. 11000101<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 11000101
- Positions: \(2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^7 + 1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\)
\(= 128 + 64 + 0 + 0 + 0 + 4 + 0 + 1\)
\(= 197\)
- Answer: 11000101<sub>(2)</sub> = 197<sub>(10)</sub>
15. 11010010<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 11010010
- Positions: \(2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^7 + 1 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0\)
\(= 128 + 64 + 0 + 16 + 0 + 0 + 2 + 0\)
\(= 210\)
- Answer: 11010010<sub>(2)</sub> = 210<sub>(10)</sub>
16. 1010100<sub>(2)</sub> = ?<sub>(10)</sub>
- Binary: 1010100
- Positions: \(2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 2^0\)
- Calculation:
\(1 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0\)
\(= 64 + 0 + 16 + 0 + 4 + 0 + 0\)
\(= 84\)
- Answer: 1010100<sub>(2)</sub> = 84<sub>(10)</sub>
---
Final Answers:
1. 145<sub>(10)</sub> = 10010001<sub>(2)</sub>
2. 124<sub>(10)</sub> = 1111100<sub>(2)</sub>
3. 242<sub>(10)</sub> = 11110010<sub>(2)</sub>
4. 116<sub>(10)</sub> = 1110100<sub>(2)</sub>
5. 182<sub>(10)</sub> = 10110110<sub>(2)</sub>
6. 70<sub>(10)</sub> = 1000110<sub>(2)</sub>
7. 238<sub>(10)</sub> = 11101110<sub>(2)</sub>
8. 164<sub>(10)</sub> = 10100100<sub>(2)</sub>
9. 10010110<sub>(2)</sub> = 150<sub>(10)</sub>
10. 10001011<sub>(2)</sub> = 139<sub>(10)</sub>
11. 1100111<sub>(2)</sub> = 103<sub>(10)</sub>
12. 1100100<sub>(2)</sub> = 100<sub>(10)</sub>
13. 1000000<sub>(2)</sub> = 64<sub>(10)</sub>
14. 11000101<sub>(2)</sub> = 197<sub>(10)</sub>
15. 11010010<sub>(2)</sub> = 210<sub>(10)</sub>
16. 1010100<sub>(2)</sub> = 84<sub>(10)</sub>
Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & 10010001 \\
2. & 1111100 \\
3. & 11110010 \\
4. & 1110100 \\
5. & 10110110 \\
6. & 1000110 \\
7. & 11101110 \\
8. & 10100100 \\
9. & 150 \\
10. & 139 \\
11. & 103 \\
12. & 100 \\
13. & 64 \\
14. & 197 \\
15. & 210 \\
16. & 84 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of decimal to binary worksheet.
