KS3 · Computer Science
Binary to denary conversion
To you, 101 means one hundred and one. To a computer, it means five. By the end of this lesson you'll know why.
Computer Science · Binary
Eight switches, one number
Each box is one bit: a binary digit, 0 or 1. The small number above each box is its place value. Tap a bit to flip it and watch the denary value change.
Why binary?
Reason it through
Why do computers count in binary instead of denary?
First link · your turn
A computer stores and processes data using electronic circuits. How many states does the circuit use to hold data?
Computer Science · Algorithms
Trace table — dry run the code
Now the other way: turn the denary number 45 into 8-bit binary. At each place value, from 128 down to 1, ask one question: does it fit into what is left?
Ready when you are — step through one line at a time.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Computers count with just 0 and 1. Learn to read their numbers and write your own.
What you need to know
- Denary (decimal) is base 10: it uses the ten digits 0 to 9, and each place value is ten times the one to its right (1, 10, 100, 1000 …).
- Binary is base 2: it uses only the digits 0 and 1, and each binary digit is called a bit.
- Computers use binary because their electronic circuits store and process data as two states: on and off.
- In binary each place value is double the one to its right. In 8 bits, from right to left, they are 1, 2, 4, 8, 16, 32, 64 and 128.
- Binary to denary: write the place values above the bits and add the place values of every column holding a 1. Columns holding 0 add nothing.
- Denary to binary: start at the largest place value. If it fits into what is left, write 1 and subtract it; otherwise write 0. Carry on until every column is filled and nothing is left.
- A byte is a group of 8 bits. It can represent the denary values 0 (00000000) to 255 (11111111).
The big picture
Binary is place value with one rule changed. Denary (base 10) uses the digits 0 to 9, and each place value is ten times the one to its right. Binary (base 2) uses only 0 and 1, called bits, and each place value is double the one to its right. Computers use binary because their circuits store and process data as two states, on and off. To read binary, add the place values of the columns holding a 1. To write it, work down from 128, writing 1 and subtracting whenever a place value fits. One byte (8 bits) holds 0 to 255.
Key points
Worked example
Problem
Convert the denary number 200 to 8-bit binary, then check your answer by converting it back.
⚠ Watch out
Reading a binary number as if it were denary, so thinking 101 means one hundred and one. In binary, 101 is 4 + 1 = 5. The other trap is adding up every place value: only the columns holding a 1 count, and a 0 column adds nothing.
Memory hook
Picture a row of eight light switches labelled 128, 64, 32, 16, 8, 4, 2, 1. Lights on count, lights off don't. Every light on: 255.
Check yourself
Without scrolling up: what is 00010110 in denary? What is 19 as an 8-bit binary number? What is the largest number one byte can hold? (Answers: 22, 00010011 and 255.)
Flashcards
(14)What is denary?
In denary, how does each place value compare with the one to its right?
What is binary?
What is a bit?
Why do computers use binary?
In binary, how does each place value compare with the one to its right?
List the place values of an 8-bit binary number, from left to right.
How do you convert a binary number to denary?
What does a column holding 0 add to the total?
How do you convert a denary number to binary?
When converting denary to binary, when do you stop?
Does the binary number 101 mean one hundred and one?
What is a byte?
What range of denary values can one byte hold?
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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Keep me postedMore KS3 Computer Science topics
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- Adding binary numbers
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- Building truth tables
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- Collecting and recording data
- Comparing sorting algorithms
- Compressing data
- Creating a 3D animation
- Decomposition: splitting problems up
- Designing a mobile app
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