How do I convert binary to hexadecimal?

Split the binary number into groups of 4 digits starting from the right and convert each group into one hex symbol. Every 4 bits equal one symbol.

How do I convert hexadecimal to decimal?

Turn each symbol into 4 bits and add the weights of the 1s, or multiply each digit by powers of 16. For example C6 = 12×16 + 6 = 198.

Unit 6 · Lesson 2

Hexadecimal

5 steps. Each one is a short story and a question to answer.

Ordinary digits stop at 9. What if we want to count higher without writing two digits?

Hexadecimal is a counting system with 16 symbols: the digits 0 to 9 and the letters A to F.

The six letters take values: A=10, B=11, C=12, D=13, E=14, F=15.

We write a small 16 next to the number to show it is hexadecimal, like A4₁₆.

Symbol

Decimal value

Hexadecimal = 16 symbols: 0 to 9 and A to F (A=10 ... F=15)

What is the value of the letter C in hexadecimal?

Pick an answer

The same number can be written three ways: decimal, binary and hexadecimal.

Every hex digit matches exactly 4 bits: for example 9 = 1001 and A = 1010.

And F = 1111, and C = 1100.

And 16 in decimal is written 10000 in binary and 10 in hexadecimal.

Decimal

Binary = Hex

1001 = 9

1010 = A

1100 = C

1111 = F

10000 = 10

Every hex symbol = 4 bits

The symbol F in binary equals...

Pick an answer

You have the long binary number 10011010. Let's shorten it to two symbols.

Split it into groups of 4 digits, starting from the right: 1001 and 1010.

Convert each group: 1001 = 9, and 1010 = 10, which is A.

Write them in order: 9A. So 10011010₂ = 9A₁₆.

1001 | 1010 = 9 | A

10011010₂ = 9A₁₆

Binary to hex: split into groups of 4 from the right and convert each

From which side do we start splitting a binary number into groups of 4?

Pick an answer

This time the opposite way: you have A4 and want it in binary.

Convert each symbol separately into 4 bits: A = 1010.

Then 4 = 0100.

Write them one after another in order: 10100100. So A4₁₆ = 10100100₂.

A= 1010

4= 0100

Result10100100

Hex to binary: turn each symbol into 4 bits and write them in order

How many bits does each hex symbol turn into?

Pick an answer

Last conversion: what does C6 in hexadecimal equal in decimal?

First turn it into binary: C = 1100 and 6 = 0110, so 11000110.

Second, add the weights of the 1s: 128 + 64 + 4 + 2.

The result is 198. Or directly: 12×16 + 6 = 198.

hex -> decimal

Hex to decimal: go through binary and add weights, or multiply by powers of 16

What is C6 in hexadecimal, in decimal?

Pick an answer

Done, see the summary

Hexadecimal

Scroll down ↓ to continue

The lesson on one page

Every idea in the lesson with its rule, ready to screenshot and revise from.

1
Hexadecimal and its symbols
Hexadecimal = 16 symbols: 0 to 9 and A to F (A=10 ... F=15)
2
Comparing the three systems
Every hex symbol = 4 bits
3
Binary to hexadecimal
Binary to hex: split into groups of 4 from the right and convert each
Hexadecimal to binary
Hex to binary: turn each symbol into 4 bits and write them in order
5
Hexadecimal to decimal
Hex to decimal: go through binary and add weights, or multiply by powers of 16

Test yourself

One question from every step. Answer and see your score.

Question 1 of 5

What is the value of the letter C in hexadecimal?

Watch and listen

Quick reel

Unit 6

Learn the hexadecimal system and its symbols 0 to F, and how to convert between hexadecimal, binary and decimal easily, in an animated explainer.

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The lesson in writing

The same explanation as the 3D scene, written out for quick review.

Hexadecimal and its symbols

Hexadecimal = 16 symbols: 0 to 9 and A to F (A=10 ... F=15). Hexadecimal is a counting system with 16 symbols: the digits 0 to 9 and the letters A to F. The six letters take values: A=10, B=11, C=12, D=13, E=14, F=15.

Page 96

Comparing the three systems

Every hex symbol = 4 bits. Every hex digit matches exactly 4 bits: for example 9 = 1001 and A = 1010. And F = 1111, and C = 1100.

Page 96

Binary to hexadecimal

Binary to hex: split into groups of 4 from the right and convert each. Split it into groups of 4 digits, starting from the right: 1001 and 1010. Convert each group: 1001 = 9, and 1010 = 10, which is A.

Page 97

Hexadecimal to binary

Hex to binary: turn each symbol into 4 bits and write them in order. Convert each symbol separately into 4 bits: A = 1010. Then 4 = 0100.

Page 97, 98

Hexadecimal to decimal

Hex to decimal: go through binary and add weights, or multiply by powers of 16. First turn it into binary: C = 1100 and 6 = 0110, so 11000110. Second, add the weights of the 1s: 128 + 64 + 4 + 2.

Page 98, 101

Questions about this lesson

What is the hexadecimal system?: A counting system with 16 symbols: the digits 0 to 9 and the letters A to F.
What are the values of A, B, C, D, E and F?: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
How do I convert binary to hexadecimal?: Split the binary number into groups of 4 digits starting from the right and convert each group into one hex symbol. Every 4 bits equal one symbol.
How do I convert hexadecimal to decimal?: Turn each symbol into 4 bits and add the weights of the 1s, or multiply each digit by powers of 16. For example C6 = 12×16 + 6 = 198.