How to Convert Binary to Hexadecimal

Step-by-Step Guide

1. 1

   Step 1: Find a line of up to four binary numbers to convert.

   Binary numbers can only be 1 and
   0.
   
   Hexadecimal numbers can be 0-9, or A-F, since hexadecimal is base-16.
   
   You can convert any binary string to hexadecimal (1, 01, 101101, etc.), but you need four numbers to make the conversion (0101→5; 1100→C, etc.).
   
   For this lesson, start with the example
   1010. 1010 If you don't have 4 digits, add zeros to the front to make it four digits.
   
   So, 01 would become
   0001., Each of the four numbers signifies a type of number decimal system number.
   
   The last digit is the one's place.
   
   You will make sense of the rest of the digits in the next step.
   
   For now, write a small one above the last digit.1010 10101{\displaystyle 1010^{1}} Note that you are not raising anything to any power
   -- this is just a way to see what digit means what. , These are the rest of your place holders.
   
   If you're curious, this is because each digit represents a different power of
   2.
   
   The first is 23{\displaystyle 2^{3}}, the second 22{\displaystyle 2^{2}}, etc. 1010 18041201{\displaystyle 1^{8}0^{4}1^{2}0^{1}} , Luckily, this conversion is easy once you have four numbers and know what they all mean.
   
   If you have a one in the first number, you have one eight.
   
   If you have a zero in the second column, you have no fours.
   
   The third column tells you how many twos, and the second how many ones.
   
   So, for our example:1010 18041201{\displaystyle 1^{8}0^{4}1^{2}0^{1}} 8 0 2 0 , Once you have your new hexadecimal numbers, simply add them up. 1010 18041201{\displaystyle 1^{8}0^{4}1^{2}0^{1}} 8 0 2 0 8+0+2+0=10{\displaystyle 8+0+2+0=10} Final answer:
   The binary number 1010 converts to A in the hexadecimal system. , This is so you don't get confused when reading hexadecimal ("is that a 1 and a 5, or a 15?").
   
   Luckily, the system is super easy, since you can't have a hexadecimal number bigger than
   15.
   
   Simply start the alphabet with 10, so that: 10=A{\displaystyle 10=A} 11=B{\displaystyle 11=B} 12=C{\displaystyle 12=C} 13=D{\displaystyle 13=D} 14=E{\displaystyle 14=E} 15=F{\displaystyle 15=F} , The following examples have answers in white beneath them.
   
   To see the work and the answers, highlight the area under the question by clicking and dragging your mouse over it.
   
   Convert 1 to hexadecimal.
   
   Add zeros to get four digits: 0001 Find your place holders: 08040211{\displaystyle 0^{8}0^{4}0^{2}1^{1}} Add up the digits: 0+0+0+1=1{\displaystyle 0+0+0+1=1} Final answer: 1 Convert 0101 to hexadecimal.
   
   Add zeros to get four digits: 0101 Find your place holders: 08140211{\displaystyle 0^{8}1^{4}0^{2}1^{1}} Add up the digits: 0+4+0+1=5{\displaystyle 0+4+0+1=5} Final answer: 5 Convert 1110 to hexadecimal.
   
   Add zeros to get four digits: 1110 Find your place holders: 18141201{\displaystyle 1^{8}1^{4}1^{2}0^{1}} Add up the digits: 8+4+2+0=14{\displaystyle 8+4+2+0=14} Final answer:
   E Convert 0011 to hexadecimal.
   
   Add zeros to get four digits: 0011 Find your place holders: 18041211{\displaystyle 1^{8}0^{4}1^{2}1^{1}} Add up the digits: 8+0+2+1=11{\displaystyle 8+0+2+1=11} Final Answer:
   B
2. 2

   Step 2: Write a small "1" above the last digit.

3. 3

   Step 3: Write a small "2" above the third digit

4. 4

   Step 4: a "4" above the second

5. 5

   Step 5: and an "8" above the first.

6. 6

   Step 6: Count out how many of each "place" you have.

7. 7

   Step 7: Add your four numbers together.

8. 8

   Step 8: Change any number above "9" into a letter.

9. 9

   Step 9: Try a few examples to get better at converting.

Detailed Guide

About the Author