Hexadecimal Numbers
Hexadecimal numbers (also known as base-16) are a system of numbers which have 16 digits, instead of 10. These digits are
where is 10, is 11, etc.
In hexadecimal, place value is determined by powers of 16, instead of 10. For example,
Determine the value of in base 10.
is equal to
Therefore, the answer is
Now that you have learned about hexadecimal numbers, give this problem a try:
Find the sum of and in base 16.
We will first convert these numbers to decimal (base 10) and work out the sum, and at the end we will convert back:
Now we need to find the sum of and , which is .
Finally we convert back. Since the answer is
However, with a lot of practice, the sum can also be done without changing the base back to 10. For instance,
Find the sum of and in base 16.
We have
Note all numbers in this segment are in base 16.
Multiplication will be complicated as instead of a multiplication chart, we have a one. Much harder!
Look at the following example:
Find the product of and in base 16.
We have
In base 10, we have just calculated