10. Converting between hexadecimal and binary
It has been mentioned earlier, hex is mainly used in computing as a very convenient way of expressing a binary number in a compact form. It is quite straightforward to move between hex and binary numbers.
HEXADECIMAL AND BINARY NUMBERS
Hex numbers run from 0 to F or 15 decimal
15 decimal is the same as 1111 binary i.e. the largest value of a nibble
So, F hex is the same as 1111 binary
If two hexadecimal digits are used, then you simply need to combine two nibbles together to produce the equivalent binary number
As we are so familiar with decimal numbers, it is easier to use this as the in-between stage
Example 1: what is E3 Hex as a binary number?
Take the first hex digit and convert this into a binary nibble
So.... 3 Hex = 3 decimal = 0011 binary
Then take the second hex digit and convert this as well into a binary nibble
So... E hex = 15 decimal = 1110 binary
Now combine the two in the right order like this: 11100011 which is the answer
Example 2: What is 11011110 as a hex number?
Split the binary number into nibbles, like this
1101 ...... 1110
Now convert each nibble into decimal ..
then finally convert these directly to hex
D ...... E
Answer: 11011110 binary = DE Hex
Challenge see if you can find out one extra fact on this topic that we haven't already told you
Click on this link: binary conversion
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