Data Representation · StudentHub Lesson
Binary numbers
How computers represent numbers with 0s and 1s.
18 minBeginner
01
What you will learn
- Explain why computers use binary
- Convert binary to denary
- Convert denary to binary
- Understand bits and bytes
- Add simple binary numbers
02
Watch the lesson
We haven’t confirmed a lesson video that matches this topic closely enough yet, so the notes below are the lesson for now. A recommended video will be added once we’ve checked one properly.
03
Topic notes
Main Idea
Computers store all data as binary — sequences of 0s and 1s — because their circuits have two states: off and on.
Key Concepts
- Each binary place value doubles: 1, 2, 4, 8, 16, 32, 64, 128
- A bit is one binary digit; a byte is 8 bits
- 8 bits can store 256 values (0–255)
- To convert to denary, add the place values with a 1
- Binary addition: 1 + 1 = 10 (write 0, carry 1)
Definitions
- Bit: A single binary digit, 0 or 1.
- Byte: A group of 8 bits.
- Denary: The base-10 number system we use every day.
Worked Example
Convert 1011 from binary to denary.
- Place values from right: 1, 2, 4, 8
- Digits 1,0,1,1 give 8 + 0 + 2 + 1
- Add them
Answer: 11
Common Mistakes
- Reading place values left-to-right starting at 1
- Forgetting to carry in binary addition
- Thinking a byte is 10 bits
04
Key concepts
Each binary place value doubles: 1, 2, 4, 8, 16, 32, 64, 128A bit is one binary digit; a byte is 8 bits8 bits can store 256 values (0–255)To convert to denary, add the place values with a 1Binary addition: 1 + 1 = 10 (write 0, carry 1)
05
Important terms
- Bit
- A single binary digit, 0 or 1.
- Byte
- A group of 8 bits.
- Denary
- The base-10 number system we use every day.
06
Worked examples
Problem
Convert 1011 from binary to denary.
- 1. Place values from right: 1, 2, 4, 8
- 2. Digits 1,0,1,1 give 8 + 0 + 2 + 1
- 3. Add them
Answer: 11
07
Quick revision
- Two states: on/off
- Place values double
- Bit = 1 digit, byte = 8 bits
- 8 bits: 0–255
- 1 + 1 = 10 in binary
08
Check your understanding
Question 1 · Multiple choice
What is binary 1000 in denary?
Question 2 · Short answer
How many bits are in a byte?
Question 3 · True or false
The largest number 8 bits can store is 255.
Done with Binary numbers?
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