# Unit 1 Section 2 : Adding and Subtracting Binary Numbers

It is possible to add and subtract binary numbers in a similar way to base 10 numbers.

For example, 1 + 1 + 1 = 3 in base 10 becomes 1 + 1 + 1 = 11 in binary.

In the same way, 3 – 1 = 2 in base 10 becomes 11 – 1 = 10 in binary.

When you add and subtract binary numbers you will need to be careful when 'carrying' or 'borrowing' as these will take place more often.

 Key Addition Results for Binary Numbers 1 + 0 = 1 1 + 1 = 10 1 + 1 + 1 = 11 Key Subtraction Results for Binary Numbers 1 – 0 = 1 10 – 1 = 1 11 – 1 = 10

## Example 1

Calculate, using binary numbers:

 (a) 111 + 100 (b) 101 + 110 (c) 1111 + 111

## Example 2

Calculate the binary numbers:

 (a) 111 – 101 (b) 110 – 11 (c) 1100 – 101

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.
Question 1
Calculate the binary numbers:
 (a) 11 + 1 (b) 11 + 11 (c) 111 + 11 (d) 111 + 10 (e) 1110 + 111 (f) 1100 + 110 (g) 1111 + 10101 (h) 1100 + 11001 (i) 1011 + 1101 (j) 1110 + 10111 (k) 1110 + 1111 (l) 11111 + 11101
Question 2
Calculate the binary numbers:
 (a) 11 – 10 (b) 110 – 10 (c) 1111 – 110 (d) 100 – 10 (e) 100 – 11 (f) 1000 – 11 (g) 1101 – 110 (h) 11011 – 110 (i) 1111 – 111 (j) 110101 – 1010 (k) 11011 – 111 (l) 11110 – 111
Question 3
Calculate the binary numbers:
 (a) 11 + 11 (b) 111 + 111 (c) 1111 + 1111 (d) 11111 + 11111
 What will be the next number that will fit this pattern?
Question 4
Calculate the binary numbers:
 (a) 10 + 10 (b) 100 + 100 (c) 1000 + 1000 (d) 10000 + 10000
 What is the next number that will continue your binary pattern?
Question 5
Solve the following equations, where all numbers, including x, are binary:
 (a) x + 11 = 1101 x = (b) x – 10 = 101 x = (c) x – 1101 = 11011 x = (d) x + 1110 = 10001 x = (e) x + 111 = 11110 x = (f) x – 1001 = 11101 x =
Question 6
Calculate the binary numbers:
 (a) 10 – 1 (b) 100 – 1 (c) 1000 – 1 (d) 10000 – 1
 What will be the next number that will fit this pattern?
Question 7
A 4-digit binary number has 2 zeros and 2 ones.
(a) Convert the binary numbers 11101 and 1110 to base 10.
and
(b) Add together the two base 10 numbers.
(c) Add together the two binary numbers.
 (b)
Question 8
A binary number has 8 digits and is to be converted to base 10.
(a) Convert the binary numbers 11101 and 10111 to base 10.
and
(b) Calculate the difference between the two base 10 numbers.