Decimal to binary questions with solutions is given here to practice decimal to binary conversions. After knowing how to convert a base-10 number into a base-2 number, these questions will help you practice number system conversions.
There are different types of numbers in the number system:
- Decimal Numbers – base 10
- Binary numbers – base 2
- Octal numbers – base 8
- Hexadecimal numbers – base 16.
Steps to convert decimal to binary numbers:
|
Step I: Divide the given number by 2. Note the remainders obtained. Step II: For an even number, the remainder is 0, and for an odd number, the remainder is 1. Step III: Successively divide the obtained result by 2 and note the remainders till the last dividend is 1. Step IV: The binary equivalent of the decimal number is obtained by writing the remainders in reverse order – MSB (Most Significant Bit) to LSB (Least Significant Bit). |
Decimal to Binary Conversions Questions with Solution
Solve the following questions to practice decimal to binary conversions.
Question 1: Convert 27810 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
278 ÷ 2 |
139 |
0 |
0 (LSB) |
|
139 ÷ 2 |
69 |
1 |
1 |
|
69 ÷ 2 |
34 |
1 |
1 |
|
34 ÷ 2 |
17 |
0 |
0 |
|
17 ÷ 2 |
8 |
1 |
1 |
|
8 ÷ 2 |
4 |
0 |
0 |
|
4 ÷ 2 |
2 |
0 |
0 |
|
2 ÷ 2 |
1 |
0 |
0 |
|
1 ÷ 2 |
0 |
1 |
1 (MSB) |
∴ (278)10 = (100010110)2
Also check with decimal to binary calulator.
Question 2: Convert 18010 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
180 ÷ 2 |
90 |
0 |
0(LSB) |
|
90 ÷ 2 |
45 |
0 |
0 |
|
45 ÷ 2 |
22 |
1 |
1 |
|
22 ÷ 2 |
11 |
0 |
0 |
|
11 ÷ 2 |
5 |
1 |
1 |
|
5 ÷ 2 |
2 |
1 |
1 |
|
2 ÷ 2 |
1 |
0 |
0 |
|
1 ÷ 2 |
0 |
1 |
1(MSB) |
∴ (180)10 = (10110100)2
Question 3: `Convert 5610 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
56 ÷ 2 |
28 |
0 |
0(LSB) |
|
28 ÷ 2 |
14 |
0 |
0 |
|
14 ÷ 2 |
7 |
0 |
0 |
|
7 ÷ 2 |
3 |
1 |
1 |
|
3 ÷ 2 |
1 |
1 |
1 |
|
1 ÷ 2 |
0 |
1 |
1 |
∴ (56)10 = (111000)2
Question 4: Convert 107310 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
1073 ÷ 2 |
536 |
1 |
1 (LSB) |
|
536 ÷ 2 |
268 |
0 |
0 |
|
268 ÷ 2 |
134 |
0 |
0 |
|
134 ÷ 2 |
67 |
0 |
0 |
|
67 ÷ 2 |
33 |
1 |
1 |
|
33 ÷ 2 |
16 |
1 |
1 |
|
16 ÷ 2 |
8 |
0 |
0 |
|
8 ÷ 2 |
4 |
0 |
0 |
|
4 ÷ 2 |
2 |
0 |
0 |
|
2 ÷ 2 |
1 |
0 |
0 |
|
1 ÷ 2 |
0 |
1 |
1 |
∴ (1073)10 = (10000110001)2
Question 5: Convert 8110 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
81 ÷ 2 |
40 |
1 |
1(LSB) |
|
40 ÷ 2 |
20 |
0 |
0 |
|
20 ÷ 2 |
10 |
0 |
0 |
|
10 ÷ 2 |
5 |
0 |
0 |
|
5 ÷ 2 |
2 |
1 |
1 |
|
2 ÷ 2 |
1 |
0 |
0 |
|
1 ÷ 2 |
0 |
1 |
1(MSB) |
∴ (81)10 = (1010001)2
Also Read:
- Binary to Decimal Conversion
- Octal to Binary Conversion
- Hexadecimal to Binary Conversion
- Hexadecimal to Decimal Conversion
Question 6: Convert 40310 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
403 ÷ 2 |
201 |
1 |
1(LSB) |
|
201 ÷ 2 |
100 |
1 |
1 |
|
100 ÷ 2 |
50 |
0 |
0 |
|
50 ÷ 2 |
25 |
0 |
0 |
|
25 ÷ 2 |
12 |
1 |
1 |
|
12 ÷ 2 |
6 |
0 |
0 |
|
6 ÷ 2 |
3 |
0 |
0 |
|
3 ÷ 2 |
1 |
1 |
1 |
|
1 ÷ 2 |
0 |
1 |
1(MSB) |
∴ (403)10 = (110010011)2
Question 7: Convert 50810 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
508 ÷ 2 |
254 |
0 |
0(LSB) |
|
254 ÷ 2 |
127 |
0 |
0 |
|
127 ÷ 2 |
63 |
1 |
1 |
|
63 ÷ 2 |
31 |
1 |
1 |
|
31 ÷ 2 |
15 |
1 |
1 |
|
15 ÷ 2 |
7 |
1 |
1 |
|
7 ÷ 2 |
3 |
1 |
1 |
|
3 ÷ 2 |
1 |
1 |
1 |
|
1 ÷ 2 |
0 |
1 |
1(MSB) |
∴ (508)10 = (111111100)2
Question 8: Convert 11110 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
111 ÷ 2 |
55 |
1 |
1(LSB) |
|
55 ÷ 2 |
27 |
1 |
1 |
|
27 ÷ 2 |
13 |
1 |
1 |
|
13 ÷ 2 |
6 |
1 |
1 |
|
6 ÷ 2 |
3 |
0 |
0 |
|
3 ÷ 2 |
1 |
1 |
1 |
|
1 ÷ 2 |
0 |
1 |
1(MSB) |
∴ (111)10 = (1101111)2
Question 9: Convert 127810 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
1278 ÷ 2 |
639 |
0 |
0(LSB) |
|
639 ÷ 2 |
319 |
1 |
1 |
|
319 ÷ 2 |
159 |
1 |
1 |
|
159 ÷ 2 |
79 |
1 |
1 |
|
79 ÷ 2 |
39 |
1 |
1 |
|
39 ÷ 2 |
19 |
1 |
1 |
|
19 ÷ 2 |
9 |
1 |
1 |
|
9 ÷ 2 |
4 |
1 |
1 |
|
4 ÷ 2 |
2 |
0 |
0 |
|
2 ÷ 2 |
1 |
0 |
0 |
|
1 ÷ 2 |
0 |
1 |
1(MSB) |
∴ (1278)10 = (10011111110)2
Question 10: Convert 14510 into a binary number.
Solution:
|
Division by 2 |
Quotient |
Remainder |
Binary Bit |
|
145 ÷ 2 |
72 |
1 |
1 (LSB) |
|
72 ÷ 2 |
36 |
0 |
0 |
|
36 ÷ 2 |
18 |
0 |
0 |
|
18 ÷ 2 |
9 |
0 |
0 |
|
9 ÷ 2 |
4 |
1 |
1 |
|
4 ÷ 2 |
2 |
0 |
0 |
|
2 ÷ 2 |
1 |
0 |
0 |
|
1 ÷ 2 |
0 |
1 |
1 (MSB) |
∴ (145)10 = (10010001)2
Related Articles: | |
|---|---|
Practice Questions on Decimal to Binary Conversions
1. Convert 15510 into a binary number.
2. Convert 37510 into a binary number.
3. Convert 100010 into a binary number.
4. Convert 1001110 into a binary number.
5. Convert 7410 into a binary number.
Keep visiting BYJU’S to get more such Maths lessons in a simple, concise and easy to understand way. Also, register at BYJU’S – The Learning App to get complete assistance for Maths preparation with video lessons, notes, tips and other study materials.
Comments