As people we count in denary which is a number system with a base ten.

Computers count in binary which is a number system with a base two.

Computers use binary to present and manipulate data.

To convert a denary value into binary

Draw a table such as the one below:

 128 64 32 16 8 4 2 1

If we are converting the number 155

first we minus the largest binary number that goes into 155. In this case we do 155-128 to get 27. In addition we make a note on the table like below:

 128 64 32 16 8 4 2 1 1

We find the largest number that 27 can be subtracted by.

We cannot use 64

We cannot use 32

We subtract 27 by 16 to get 11 and make a note on the table:

 128 64 32 16 8 4 2 1 1 1

We then subtract 11 by 8 to get 3 and make a note on the table:

 128 64 32 16 8 4 2 1 1 1 1

We then find the largest number that 3 can be subtracted by :

We cannot use 8

We cannot use 4

We can subtract 3 by 2 to get 1 and make a note on the table

 128 64 32 16 8 4 2 1 1 1 1 1

We then subtract 1 by 1 to get 0 and make a note on the table .

 128 64 32 16 8 4 2 1 1 1 1 1 1

Finally we fill the blanks in with zeros:

 128 64 32 16 8 4 2 1 1 0 0 1 1 0 1 1

155 is equal to 10011011 in binary

To convert binary into denary

We will convert the binary number 01010011

Draw out the table below and fill the binary number

 128 64 32 16 8 4 2 1 0 1 0 1 0 0 1 1

Add the numbers with the values 1 so

64+16+2+1=83

01010011 = 83

Scroll to Top