Binary Arithmetic

MULTIPLICATION

Shift & Add

 

To do multiplication you need to remember your times tables. In binary there are not very many to remember

 

0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1

 

Example 1

 

1101 x 10 is the same as 13 x 2 in decimal

 

						1	1	0	1	x
								1	0
					1	1	0	1	0

 

When you multiply by a power of 2, ie 1,2,4,8,16… this just like adding zeros to a binary number.

You are multiplying by 1,10,100,1000,10000…..

 

Example 2

 

1101 x 101 is the same as multiplying 13 x 5 in decimal

 

 

						1	1	0	1	x
							1	0	1
						1	1	0	1
									0
								0	0

 

Set out the multiplication neatly making sure that the numbers are written directly under each other.

There are three lines before the final answer as there are three digits in 101.

To make sure that you shift the numbers to the left the correct number of places, write in the zeros after completing the first line.

 

						1	1	0	1	x
							1	0	1
						1	1	0	1
									0
				1	1	0	1	0	0

 

Now perform the addition

 

						1	1	0	1	x
							1	0	1
						1	1	0	1
									0
				1	1	0	1	0	0
			1	0	0	0	0	0	1

 

 

Example 3

 

This will have four lines of numbers to add

 

					1	1	1	0	1	x
						1	1	0	1
					1	1	1	0	1
									0
			1	1	1	0	1	0	0
		1	1	1	0	1	0	0	0
	1	0	1	1	1	1	0	0	1