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Year 10
AQA

Number bases

I know the difference between base-2 and base-10 numbers and I can convert between these bases.

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New
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Year 10
AQA

Number bases

I know the difference between base-2 and base-10 numbers and I can convert between these bases.

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Lesson details

Key learning points

  1. Number systems use place value to represent the value of each digit in a number.
  2. The base of a number system refers to the range of values a digit can take.
  3. Decimal is a base-10 number system.
  4. Binary is a base-2 number system.

Keywords

  • Place value - a digit's value based on its position in a number

  • Base-10 - number system using digits 0-9, where each place value is a power of ten

  • Base-2 - number system using only the digits 0 and 1, where each place value is a power of two

  • Decimal - a base-10 numbering system

Common misconception

Pupils may think the place value for binary is the same as decimal in the fact each place value to the left is 10 times greater.

Binary place values double. So the first bit has the place value of 1 and the second has the place value of 2 and so on.

Encourage pupils to use the conversion tables when converting between binary and decimal and vice versa. Even though they can be done without, pupils make mistakes with visualising the place value order.
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equipment-required

Equipment

Pupils do not require any specific equipment for this lesson.

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Licence

This content is © Oak National Academy Limited (2025), licensed on
Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
What does the term 'data' mean in computing?
information after it has been processed
instructions for completing a task
Correct answer: raw facts, such as numbers or text, presented without meaning
the result of a calculation
Q2.
What is a transistor?
a type of binary digit
a part of a number system
a way to convert decimal numbers into binary
Correct answer: a tiny electronic switch controlled by electricity
Q3.
In a binary system, if on is represented by 1, what represents off?
Correct Answer: 0, zero
Q4.
Why do computers use binary to represent data?
because binary is easy for humans to understand
Correct answer: because binary can be represented by two-state electrical signals
because binary numbers are always smaller than decimal numbers
because binary uses more digits than decimal
Q5.
What is the highest-value digit in binary?
Correct Answer: 1, one
Q6.
Match the words to their correct description.
Correct Answer:data,raw facts, such as numbers or text, presented without any meaning
tick

raw facts, such as numbers or text, presented without any meaning

Correct Answer:binary,a number system that uses the digits 0 and 1 to represent data
tick

a number system that uses the digits 0 and 1 to represent data

Correct Answer:instructions,directions on how to carry out a specific task
tick

directions on how to carry out a specific task

Correct Answer:transistor,a tiny electronic switch controlled by electricity
tick

a tiny electronic switch controlled by electricity

Exit quiz

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6 Questions

Q1.
What is the base of the binary number system?
Correct answer: 2
10
1
5
Q2.
What is a digit’s value based on its position in a number known as?
Correct Answer: place value
Q3.
What digits are used in decimal numbers?
1 and 0
Correct answer: 0 to 9
0 to 10
1 to 9
Q4.
What is the decimal value of the binary number 1101?
Correct Answer: 13, thirteen
Q5.
What is the binary representation of the decimal number 10?
Correct Answer: 1010
Q6.
Match the term to the correct description.
Correct Answer:binary place values,128, 64, 32, 16, 8, 4, 2, 1
tick

128, 64, 32, 16, 8, 4, 2, 1

Correct Answer:decimal place values,10000, 1000, 100, 10, 1
tick

10000, 1000, 100, 10, 1

Correct Answer:base-10,a number system with 0 to 9, where each place value is a power of ten
tick

a number system with 0 to 9, where each place value is a power of ten

Correct Answer:base-2,a number system with 0 and 1, where each place value is a power of two
tick

a number system with 0 and 1, where each place value is a power of two

Correct Answer:decimal,a base-10 number system
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a base-10 number system