# Converting Between Hexadecimal and Binary

As said before in an earlier post, numbers are calculated in different bases. The most used types are base two (also known as binary), base 10 (which we use mainly in mathematics), and hexadecimal, which is what we will be learning about today. As you know, there are no symbols to represent numbers that are 10 or up. So here are the following shortcuts that are used in hexadecimal.

• For numbers 0-9, use the regular 0-9
• For the number 10 – use the symbol A
• For the number 11 – use the symbol B
• For the number 12 – use the symbol C
• For the number 13 – use the symbol D
• For the number 14 – use the symbol E
• For the number 15 – use the symbol F

For example, numbers can look like 17F, 7B9, ABC, and much much more.

So why is hexadecimal used?                                                                                                   Hexadecimal is used as a simplification of binary. For example:

• In binary, 289 is represented as 0001 0010 0001
• In hexadecimal, 289 is represented as 121

As you can see, it is much easier to use hexadecimal than to use binary.

Now lets talk about the relation between binary and hexadecimal. As you know, each binary digit is known as a bit (0101 has 4 bits).  Eight of these is known as a byte (0100 0111). Lastly, a nibble is four bits (0101), which hexadecimal uses. Converting from binary to hexadecimal, every nibble is one digit in hexadecimal. Here is one example shown:

0101  1100                  First, split the binary number into different nibbles

5         12                      Convert these nibbles into base 10 numbers

5C                                Convert the base 10 numbers to hexadecimal

Here are some practice problems. Answers to these are under the Youtube video.

1. Convert 0010 1010 1010 from binary to hexadecimal
2. Convert 0010 1011 from binary to hexadecimal
3. Convert 1010100 from binary to hexadecimal
4. Convert 111001011 from binary to hexadecimal
5. Convert 50 base ten to hexadecimal (Convert to binary first)
6. Convert 829 base ten to hexadecimal

If your are still having trouble understanding this, please use this Khan Academy video that explains the concept pretty well.

1. 2AA
2. 2B
3. 54
4. 1CB
5. 32
6. 33D

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