number system conversions

Denary-Binary

To convert from Denary to Binary, draw a table showing all of the base-2 columns from 2⁰ to 2⁸

Now look at the number you are trying to convert, eg 37

Put a 1 in the table for every value that is required to make the number, or a 0 if not required.

=00100101

or just 100101

Binary-Denary

Lets convert this number to denary: 1001011

First, put it in a table with columns from 2⁰ to 2⁷, or more or less as required

Now add up all of the denary column headers wherever you find a 1:

= 64 + 8 + 2 + 1

= 75

Binary-Hex

Let's convert this binary number to hex: 101101

Starting from the right, create groups of 4 bits (nibbles):

Now, convert each nibble to a hexadecimal number:

Warning! We are converting to hexadecimal. So, don't forget to change the 13 to D!

The final answer is 2D

Hex-Binary

Let's convert this hex number to binary: F3

There are 2 hex digits and each one can be represented by a binary nibble!

We need 2 nibbles:

Now we just need to do the conversion. Remember, HEX F is the same as 15 in denary.

The final answer is: 11110011

Denary-Hex

Strategy 1

We are going to keep dividing the denary number until we end up with 0.

Let's convert this denary number to hexadecimal: 75

The process is:

• divide the number by 16 and note the result
• also, note the remainder
• divide the result by 16 and note the remainder
• repeat this process until the result is 0

Now look at the remainder column. Starting from the bottom, write out the numbers. Remember to convert any numbers above 9 into hexadecimal characters:

=4 11

=4 B

Strategy 2

First convert the decimal number to binary. Then convert the binary number to hexadecimal. This process is easier for scientists who are not so good at maths!

Hex-Denary

Similar to binary, we just need to create a table with columns from 16⁰ to 16^whatever depending on the value we are converting.

Let's convert the hexadecimal number 32B to denary:

=(3*256) + (2*16) + (11*1)

=768 + 32 + 11

=811