Binary numbers and representing text
A computer stores everything as two states. Once you can convert between denary and binary, file sizes and character sets stop being mysterious.
Lesson overview
What you'll learn in this lesson
Understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers
Key learning points
- • Place value in base two
- • Binary addition
- • Overflow
- • From numbers to text
This lesson at a glance
- 30 minutes
- 25 parts to scroll through
- 4 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 25
Watch first
Binary numbers and representing text
From switches to numbers to letters on a screen.
In a nutshell
Understand how numbers can be represented in binary, and be able to carry out simple operations on binary numbers
What you already know
Part 2 of 25
Before we start
What you already know
You should already know place value in base ten and that computers use switches that are on or off.
Key words
Part 3 of 25
Key words
Words you'll need today
- Bit
- A single binary digit, 0 or 1.
- Byte
- Eight bits, enough for 256 different patterns.
- Denary
- Ordinary base-ten counting.
- Overflow
- When a result needs more bits than are available.
- Character set
- An agreed mapping from characters to binary codes, such as ASCII.
Reset break
Part 4 of 25
Pause
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Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 5 of 25
Learning cycle 1 of 2
Counting in twos
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 6 of 25
Learn
Place value in base two
In an eight-bit number the column headings are 128, 64, 32, 16, 8, 4, 2, 1. To convert 37 you take the biggest heading that fits (32), then 4, then 1: 00100101. Converting back is simply adding the headings above each 1.
Explore the idea
Part 7 of 25
Learn
Binary addition
The rules are 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1=11 (write 1, carry 1). Line up the columns exactly as you would in denary, working right to left.
Reset break
Part 8 of 25
Pause
That's sitting 2 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 9 of 25
Quick check
Part 10 of 25
Learning cycle
Part 11 of 25
Learning cycle 2 of 2
Adding, overflow and characters
A short piece of teaching, then a check to make sure it has landed.
Reset break
Part 12 of 25
Pause
That's sitting 3 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 13 of 25
Learn
Overflow
If you only have eight bits, 11111111 + 1 needs a ninth. The carry falls off the end and the answer wraps to 00000000, which is wrong. Real systems detect this with an overflow flag; it is a limit of the storage, not of the arithmetic.
Explore the idea
Part 14 of 25
Learn
From numbers to text
Characters are stored as numbers. In ASCII, 'A' is 65 and 'a' is 97, so the gap between an upper- and lower-case letter is always 32. Unicode extends the idea to tens of thousands of characters, which is why one emoji can take more bytes than one letter.
Quick check
Part 15 of 25
Reset break
Part 16 of 25
Pause
That's sitting 4 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Quick check
Part 17 of 25
Common mix-ups
Part 18 of 25
Common mix-ups
Things people often get wrong
- Binary 10 is two, not ten.
- Eight bits give 256 patterns (0–255), not 255 patterns.
- Text is not stored 'as letters' — it is stored as numbers using an agreed character set.
Challenge round
Part 19 of 25
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Reset break
Part 20 of 25
Pause
That's sitting 5 of 6 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 21 of 25
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Characters are stored as ____.
Challenge round
Part 22 of 25
Game · Recall cards
What is 00101101 in denary?
Card 1 of 4
Exit quiz
Part 23 of 25
Exit quiz
Show what you've learned
6 questions, marked together at the end. Nothing is timed.
1. How many patterns can 8 bits hold?
2. Denary 9 in binary is...
3. A byte is...
4. 1 + 1 in binary gives...
5. Unicode exists because...
6. Lower-case 'a' in ASCII is...
Mastery quiz
Part 24 of 25
Marked quiz
End of lesson quiz: Binary numbers and representing text
4 questions, marked with the reasoning shown. No timer.
1. What is 00101101 in denary?
2. What is 1011 + 0110 in binary?
3. Overflow happens when...
4. In ASCII, if 'A' is 65 then 'C' is...
Lesson round-up
Part 25 of 25
Lesson round-up
Ready when you are
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Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 25 · Watch & discover