Number Systems Worksheets | Dynamically Created Number Systems ... - Free Printable

Let’s solve each problem step by step. We’ll convert decimal numbers to binary and binary numbers to decimal using simple methods.

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Part 1: Convert Decimal to Binary

To convert a decimal number to binary, we repeatedly divide the number by 2 and write down the remainders. Then read the remainders from bottom to top.

#### 1) 145 (decimal) → binary
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

Read remainders from bottom to top: 10010001

✔ Answer: 10010001₂

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#### 2) 124 (decimal) → binary
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

Bottom to top: 1111100

✔ Answer: 1111100₂

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#### 3) 242 (decimal) → binary
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

Bottom to top: 11110010

✔ Answer: 11110010₂

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#### 4) 116 (decimal) → binary
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

Bottom to top: 1110100

✔ Answer: 1110100₂

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#### 5) 182 (decimal) → binary
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

Bottom to top: 10110110

✔ Answer: 10110110₂

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#### 6) 70 (decimal) → binary
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

Bottom to top: 1000110

✔ Answer: 1000110₂

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#### 7) 238 (decimal) → binary
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

Bottom to top: 11101110

✔ Answer: 11101110₂

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#### 8) 164 (decimal) → binary
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

Bottom to top: 10100100

✔ Answer: 10100100₂

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Part 2: Convert Binary to Decimal

To convert binary to decimal, multiply each digit by 2 raised to its position (starting from 0 on the right), then add them up.

#### 9) 10010110₂ → decimal
Positions (from right, starting at 0):

Digit: 1 0 0 1 0 1 1 0
Position: 7 6 5 4 3 2 1 0

Calculate:
1×2⁷ = 128
0×2⁶ = 0
0×2⁵ = 0
1×2⁴ = 16
0×2³ = 0
1×2² = 4
1×2¹ = 2
0×2⁰ = 0

Add: 128 + 16 + 4 + 2 = 150

✔ Answer: 150₁₀

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#### 10) 10001011₂ → decimal
Digits: 1 0 0 0 1 0 1 1
Positions: 7 6 5 4 3 2 1 0

1×128 = 128
0×64 = 0
0×32 = 0
0×16 = 0
1×8 = 8
0×4 = 0
1×2 = 2
1×1 = 1

Add: 128 + 8 + 2 + 1 = 139

✔ Answer: 139₁₀

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#### 11) 1100111₂ → decimal
This is 7 digits → positions 6 to 0

Digits: 1 1 0 0 1 1 1
Positions: 6 5 4 3 2 1 0

1×64 = 64
1×32 = 32
0×16 = 0
0×8 = 0
1×4 = 4
1×2 = 2
1×1 = 1

Add: 64+32+4+2+1 = 103

✔ Answer: 103₁₀

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#### 12) 1100100₂ → decimal
Digits: 1 1 0 0 1 0 0
Positions: 6 5 4 3 2 1 0

1×64 = 64
1×32 = 32
0×16 = 0
0×8 = 0
1×4 = 4
0×2 = 0
0×1 = 0

Add: 64+32+4 = 100

✔ Answer: 100₁₀

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#### 13) 1000000₂ → decimal
Only first digit is 1 → position 6

1×2⁶ = 64

✔ Answer: 64₁₀

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#### 14) 11000101₂ → decimal
Digits: 1 1 0 0 0 1 0 1
Positions: 7 6 5 4 3 2 1 0

1×128 = 128
1×64 = 64
0×32 = 0
0×16 = 0
0×8 = 0
1×4 = 4
0×2 = 0
1×1 = 1

Add: 128+64+4+1 = 197

✔ Answer: 197₁₀

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#### 15) 11010010₂ → decimal
Digits: 1 1 0 1 0 0 1 0
Positions: 7 6 5 4 3 2 1 0

1×128 = 128
1×64 = 64
0×32 = 0
1×16 = 16
0×8 = 0
0×4 = 0
1×2 = 2
0×1 = 0

Add: 128+64+16+2 = 210

✔ Answer: 210₁₀

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#### 16) 1010100₂ → decimal
Digits: 1 0 1 0 1 0 0
Positions: 6 5 4 3 2 1 0

1×64 = 64
0×32 = 0
1×16 = 16
0×8 = 0
1×4 = 4
0×2 = 0
0×1 = 0

Add: 64+16+4 = 84

✔ Answer: 84₁₀

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Final Answer:

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