Unit 1 Section 3 : Multiplying Binary Numbers

Long multiplication can be carried out with binary numbers and is explored in this section.

Note that multiplying by numbers like 10, 100 and 1000 is very similar to working with base 10 numbers.

Example 1

Calculate the binary numbers:

(a)1011 × 100
(b)110110 × 1000
(c)11011 × 10000

Example 2

Calculate the binary numbers:

(a)1011 × 11
(b)1110 × 101
(c)11011 × 111
(d)11011 × 1001

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct 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 Click on this button to see the correct answer to see the answer.
Question 1
Calculate the binary numbers:
(a) 111 × 10
(b) 1100 × 100
(c) 101 × 1000
(d) 11101 × 1000
(e) 10100 ÷ 10
(f) 1100 ÷ 100
Check your answers by converting to base 10 numbers.
Question 2
Calculate the binary numbers:
(a) 111 × 11
(b) 1101 × 11
(c) 1101 × 101
(d) 1111 × 110
(e) 11011 × 1011
(f) 11010 × 1011
(g) 10101 × 101
(h) 10101 × 111
(i) 10101 × 110
(j) 100111 × 1101
Question 3
Solve the following equations, where all numbers, including x, are binary:
(a)
x  = 110
11
 x =
(b)
x  = 101
101
 x =
(c)
x  = 111
10
 x =
(d)
x  = 1011
111
 x =
Question 4
Multiply each of the following binary numbers by itself:
(a) 11
(b) 111
(c) 1111
What do you notice about your answers to parts (a), (b) and (c)?
What will you get if you multiply 11111 by itself?
Question 5
Multiply each of the following binary numbers by itself:
(a) 101
(b) 1001
(c) 10001
(d) 100001
What would you expect to get if you multiplied 1000001 by itself?
Question 6
Calculate the binary numbers:
(a) 101 (110 + 1101)
(b) 1101 (1111 – 110)
(c) 111 (1000 – 101)
(d) 1011 (10001 – 1010)
Question 7
Here are 3 binary numbers:
11011 11100 10011
Working in binary,
(a) multiply the two larger numbers,
(b) multiply the two smaller numbers.
Question 8
(a) Multiply the base 10 numbers 45 and 33.
(b) Convert your answer to a binary number.
(c) Convert 45 and 33 to binary numbers.
and
(d) Multiply the binary numbers obtained in part (c) and compare this answer with your answer to part (b).
(b)