GCSE · Computer Science · Edexcel · Spec 1CP2

Hexadecimal

#FF6600 is six characters on screen, yet the computer still holds 24 bits underneath. So what is hexadecimal for? Flip some bits and find out.

Computer Science · Data

Flip the bits, read the hexadecimal

8-bit binary 00000000 = 0 in denary, 0x00 in hex

Denary0Hex0x00

click a bit to toggle it

Eight switches, eight bits. Start with the four on the right: flip them from 0000 up to 1111 and watch the Hex readout. Four bits can make exactly 16 values, so we need 16 symbols to name them, and 0 to 9 runs out at 9. Now flip the four on the left and watch a second digit appear.

Watch out: The readout puts 0x in front of the hexadecimal digits. Ignore the 0x and read the digits after it.

Computer Science · Number representation

Swap each group of four for one digit

Pick A3 and watch the binary split into two groups of four: 1010 becomes A and 0011 becomes 3. Then work the other way: toggle bits yourself until you have made 6C, which is just 6B plus one.

Decimal

163

Binary

1010 0011

Hexadecimal

0xA3

Watch out: Make your groups of four starting from the right-hand end of the binary number, not the left.

Hexadecimal to denary

Same method, your turn: convert 3D

Hexadecimal 2F is 2 × 16 + 15 = 47 in denary. Use the same method to convert 3D. At each gap, pick the step that comes next.

Split 3D into its two digits: 3 on the left and D on the right.
missing step

Which line is step 2?

D stands for 13.D stands for 14.D stands for 4.

What is hexadecimal for?

What does hexadecimal do for the computer?

Writing FF is much quicker than writing 11111111. They name the same number.

Which of these is closest to what you think hexadecimal does for the computer?

It saves memory, because FF is shorter than 11111111.It makes the computer process numbers faster.Nothing. Hexadecimal is for people, and the computer still stores and processes the same binary.The computer finds hexadecimal easier to handle than long binary.

How sure are you?

I'm sureI think soI'm guessing

It saves memory, because FF is shorter than 11111111.

This is a common misconception

Easy to believe, and FF really is shorter on the screen. But the computer still holds the same bits underneath. The number of bits is the same, so no memory is saved. Hexadecimal changes how people write the bits, not how many there are.

It makes the computer process numbers faster.

This is a common misconception

Tempting, since there are fewer digits to look at. But the computer still processes binary data. Hexadecimal is not faster for the computer. The shorter version helps the person looking at it.

Nothing. Hexadecimal is for people, and the computer still stores and processes the same binary.

This matches the evidence

Spot on. Same bits, same number of bits, nothing for the machine to gain. What changes is how easy the number is for a person to read, write and interpret.

The computer finds hexadecimal easier to handle than long binary.

This is a common misconception

It is the other way round. Hexadecimal is easier for humans, not for the computer. The computer still stores and processes binary.

Hexadecimal is a shorthand for people. The computer holds exactly the same bits either way.

Have a go

Why write a colour as #FF6600?

A programmer writes a colour as #FF6600, a six-digit hexadecimal code, instead of the 24 binary digits it is stored as. Explain why. Then name one other place hexadecimal is used. [4 marks]

Your answer

0 words · your answer stays on this page and is not sent anywhere.

The mark scheme

Hexadecimal is shorter: six digits instead of 24 binary digits. (1 mark)
It is easier for people to read, write and interpret (or to communicate). (1 mark)
Fewer digits means errors are less likely. (1 mark)
Names one other use of hexadecimal: MAC addresses or memory dumps. (1 mark)

Model answer

Six hexadecimal digits are much shorter than 24 binary digits, so the code is easier for people to read, write and communicate. Fewer digits also makes mistakes less likely when copying or typing it. The computer still stores all 24 bits; hexadecimal is just for people. Hexadecimal is also used in MAC addresses and memory dumps.

Answer in three parts: shorter, easier for people, fewer errors. Then remember the computer still holds the same bits.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

What you need to know

Four bits can be arranged in exactly 16 different ways, from 0000 up to 1111.
Hexadecimal is base 16: its 16 digits are 0 to 9 then A to F, and each place is 16 times bigger than the one to its right.
The letters are numbers: A is 10, B is 11, C is 12, D is 13, E is 14 and F is 15.
Have a goSam says: "E is the fifth letter, so E is 5." Sam sounds very sure. What is E really worth?
14
The letters are not alphabet positions. A is 10, B is 11, C is 12, D is 13, so E is 14.
Counting carries on as normal: after 6B comes 6C, and hexadecimal 10 is 16 in denary.
Have a goKeep counting from 6C. What are the next two hexadecimal numbers?
6D, then 6E
Counting works as normal: the letter digits just carry on upwards, one at a time.
Every group of four binary digits becomes one hexadecimal digit, so 1111 (15) is F and hexadecimal is shorter.
To go from binary to hexadecimal, split into fours from the right and swap each group for its digit: 1010 0011 is A3.
Have a goTry it before you look: write 1111 0000 in hexadecimal.
F0
1111 is 15, which is F, and 0000 is 0. Each group of four gets its own digit, even a group of zeros.
To go from hexadecimal to denary, multiply each digit by its place value and add: 2F is 2 × 16 + 15 = 47.
People use hexadecimal because it is easier to read, write and interpret, and fewer digits means fewer errors.
Hexadecimal is for humans only: the computer still stores and processes binary, with the same number of bits.
You will see hexadecimal in colour codes like #FF6600, in MAC addresses and in memory dumps.

The big picture

Hexadecimal is base 16: the digits 0 to 9 and then A to F (10 to 15). One hexadecimal digit stands for exactly four bits, so binary becomes shorter and easier for people to read, write and convert. The computer still stores and processes the same binary.

Key points

1Hexadecimal is base 16: digits 0 to 9 then A to F, where A to F are the values 10 to 15.

2One hexadecimal digit stands for four bits, so 1111 is 15, which is F.

3Binary to hexadecimal: groups of four from the right. Hexadecimal to denary: digit × place value, then add.

4Hexadecimal is easier for people to read, write and interpret, and fewer digits means fewer errors.

5Hexadecimal is for humans only: the computer still stores and processes the same binary bits.

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Worked example

Problem

Convert the binary number 0111 1011 to hexadecimal, then convert that hexadecimal number to denary.

⚠ Watch out

Thinking hexadecimal saves memory or makes the computer faster. It does neither: the computer still stores and processes the same bits, and hexadecimal is only easier for people to read and write.

🧠

Memory hook

Four bits, sixteen values, one hexadecimal digit. The screen shows the short version, and the computer still holds every bit.

✓

Check yourself

Invent a two-digit hexadecimal number with a letter in it. Write it in binary, then in denary. Then say what hexadecimal does for you, but not for the computer.

Flashcards

(13)

How many different values can four bits hold?

16, from 0000 (0) up to 1111 (15).

What are the 16 digits of hexadecimal, in order?

0 1 2 3 4 5 6 7 8 9 A B C D E F.

What do the letters A, B, C, D, E and F stand for?

A is 10, B is 11, C is 12, D is 13, E is 14 and F is 15.

How much bigger is each hexadecimal place value than the one to its right?

16 times bigger, so the places are worth 1, 16 and so on.

What comes after 6B in hexadecimal? And what is hexadecimal 10 in denary?

6C, because counting carries on as normal. Hexadecimal 10 is 16 in denary, the first value that needs two digits.

Which hexadecimal digit is 1111?

F, because 1111 is 15 in denary.

How many binary digits does one hexadecimal digit stand for?

Four. Every group of four binary digits becomes one hexadecimal digit, so hexadecimal is shorter than binary.

How do you convert binary to hexadecimal?

Split into groups of four bits from the right, then swap each group for its hexadecimal digit. Reverse the steps to go from hexadecimal to binary.

Write hexadecimal 9E as binary.

9 is 1001 and E is 1110, so 9E is 1001 1110.

How do you convert hexadecimal to denary?

Multiply each digit by its place value (1, 16, …) and add the results. For example 2F is 2 × 16 + 15 = 47.

Why do people use hexadecimal instead of binary?

It is easier to read, write and interpret, and it uses fewer digits, so errors are less likely.

A colour code like #FF6600 has six characters. How many bits does the computer hold, and does hexadecimal save memory?

24 bits (six digits × four bits). Hexadecimal saves no memory and is no faster: the computer still stores and processes binary.

Name three places hexadecimal is seen.

Colour codes such as #FF6600, MAC addresses and memory dumps.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Flip the bits, read the hexadecimal

Swap each group of four for one digit

Same method, your turn: convert 3D

What does hexadecimal do for the computer?

Why write a colour as #FF6600?

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