Binary addition questions with solutions are given here to practise the addition and subtraction of binary numbers. Binary numbers are base – 2; every number in this system is expressed as 0’s and 1’s.
Other number systems are:
- Decimal Numbers – base 10
- Octal numbers – base 8
- Hexadecimal numbers – base 16.
Binary numbers are of great importance as they are used in digital electronics. The symbol 0 represents the OFF position, and 1 represents the ON position. Each symbol represents a bit used to operate any digital system like computers, calculators etc.
Like decimal numbers, we can perform the addition and subtraction of binary numbers. Following are rules for the addition of binary numbers.
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 0; carry 1
- 1 + 1 + 1 = 1; carry 1
We shall use these rules to perform the addition of binary numbers.
Learn more about Binary addition.
Binary Addition Questions with Solutions
Solve the following questions to practise binary addition.
Question 1:
Add the following binary numbers:
(i) 11010 + 11100
(ii) 101011 + 110101
Solution:
(i)
|
1 |
1 |
0 |
1 |
0 |
|
|---|---|---|---|---|---|
|
+ |
1 |
1 |
1 |
0 |
0 |
|
1 |
1 |
0 |
1 |
1 |
0 |
∴ 11010 + 11100 = 110110
(ii)
|
1 |
0 |
1 |
0 |
1 |
1 |
|
|---|---|---|---|---|---|---|
|
+ |
1 |
1 |
0 |
1 |
0 |
1 |
|
1 |
1 |
0 |
0 |
0 |
0 |
0 |
∴ 101011 + 110101 = 1100000
Question 2:
Add the following binary numbers:
(i) 11011 + 10001
(ii) 10101 + 110001
Solution:
(i)
|
1 |
1 |
0 |
1 |
1 |
|
|---|---|---|---|---|---|
|
+ |
1 |
0 |
0 |
0 |
1 |
|
1 |
0 |
1 |
1 |
0 |
0 |
∴ 11011 + 10001 = 101100
(ii)
|
1 |
0 |
1 |
0 |
1 |
||
|---|---|---|---|---|---|---|
|
+ |
1 |
1 |
0 |
0 |
0 |
1 |
|
1 |
0 |
0 |
0 |
1 |
1 |
0 |
∴ 10101 + 110001 = 1000110
Question 3:
Add the following binary numbers:
(i) 11110000 + 1000011001
(ii) 10101000 + 010001001
Solution:
(i)
|
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
|||
|---|---|---|---|---|---|---|---|---|---|---|
|
+ |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
1 |
|
1 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
∴ 11110000 + 1000011001 = 1100001001.
(ii)
|
1 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
||
|---|---|---|---|---|---|---|---|---|---|
|
+ |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
|
1 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
∴ 10101000 + 010001001 = 100110001.
Question 4:
Add the following binary numbers:
(i) 0011010 + 111001
(ii) 1010111 + 1001111
Solution:
(i)
|
0 |
0 |
1 |
1 |
0 |
1 |
0 |
|---|---|---|---|---|---|---|
|
+ |
1 |
1 |
1 |
0 |
0 |
1 |
|
1 |
0 |
1 |
0 |
0 |
1 |
1 |
∴ 0011010 + 111001 = 1010011
(ii)
|
1 |
0 |
1 |
0 |
1 |
1 |
1 |
|
|---|---|---|---|---|---|---|---|
|
+ |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
|
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
∴ 1010111 + 1001111 = 10100110.
Question 5:
Add the following binary numbers:
(i) 100001111 + 111001101
(ii) 101011111 + 110011010
Solution:
(i)
|
1 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
|
|---|---|---|---|---|---|---|---|---|---|
|
+ |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
∴ 100001111 + 111001101 = 1011011100.
(ii)
|
1 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
|
|---|---|---|---|---|---|---|---|---|---|
|
+ |
1 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
|
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
1 |
∴ 101011111 + 110011010 = 1011111001.
Also Check:
- Binary to Decimal Conversion
- Octal to Binary Conversion
- Hexadecimal to Binary Conversion
- Hexadecimal to Decimal Conversion
Question 6:
Add the following binary numbers: 11110 and 101101
Solution:
|
1 |
1 |
1 |
1 |
0 |
||
|---|---|---|---|---|---|---|
|
+ |
1 |
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
1 |
0 |
1 |
1 |
∴ 11110 + 101101 = 1001011.
|
Subtraction of Binary Numbers Subtraction in digital systems is done by adding a negative signed binary number. Computers used signed numbers to represent negative numbers. Usually, we subtract numbers by finding the two’s complement. If A and B represent two binary numbers, then, A – B = A + 2’s complement of B The subtraction of binary numbers works as given below:
|
|---|
Learn more about Binary subtraction.
Question 7:
Subtract 11010 from 111101.
Solution:
Since the minuend is of 6-bits, we make the subtrahend also of 6-bits
6-bits subtrahend = 011010
1’s complement of 011010 = 100101
2’s complement of 011010 = 1’s complement of 011010 + 1
= 100101 + 1
= 100110
Now, 111101 – (011010) = 111101 + 100110
|
1 |
1 |
1 |
1 |
0 |
1 |
|
|---|---|---|---|---|---|---|
|
+ |
1 |
0 |
0 |
1 |
1 |
0 |
|
(1) |
1 |
0 |
0 |
0 |
1 |
1 |
We see that one bit (1) is overflowing; hence, we ignore that bit
∴ 111101 – (011010) = 100011
Question 8:
Subtract 1001 from 1101.
Solution:
Using the rules of binary subtraction:
|
1 |
1 |
0 |
1 |
|
|---|---|---|---|---|
|
– |
1 |
0 |
0 |
1 |
|
0 |
1 |
0 |
0 |
∴ 1101 – 1001 = 100
Question 9:
Subtract 111001 from 1111001.
Solution:
Using the rules of binary subtraction:
|
1 |
1 |
1 |
1 |
0 |
0 |
1 |
|---|---|---|---|---|---|---|
|
– |
1 |
1 |
1 |
0 |
0 |
1 |
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
∴ 1111001 – 111001 = 1000000.
Question 10:
Subtract 100100 from 11100010 using 2’s complement.
Solution:
Since the minuend is 8-bit, we also make the subtrahend to 8-bit
8-bit subtrahend = 00100100
1’s complement of 00100100 = 11011011
2’s complement of 00100100 = 1’s complement of 00100100 + 1
= 11011011 + 1 = 11011100
Now, 11100010 – 100100 = 11100010 + 11011100
|
1 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
|
|---|---|---|---|---|---|---|---|---|
|
+ |
1 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
|
(1) |
1 |
0 |
1 |
1 |
1 |
1 |
1 |
0 |
We see that one bit (1) is overflowing; hence, we ignore that bit
∴ 11100010 – 100100 = 10111110.
You can also check your answers with a Binary operations calculator.
Related Articles: |
|
|---|---|
Practice Questions on Binary Addition
1. Add the following binary numbers:
(i) 110101 + 11010011
(ii) 100110 + 01011101
(iii) 1111 + 11000
(iv) 10011 + 11001
(v) 1100111 + 111001
2. Subtract the following binary numbers using subtraction rules:
(i) 11011 from 11110
(ii) 10101 from 11000
(iii) 111000 from 1101101
3. Subtract the following using the 2’s complement:
(i) 1100001 from 111100001
(ii) 1100 from 11111
(iii) 10001 from 101111
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.
