1. How many distinct patterns do 3 bits provide?
- 3
- 6
- 8
Check the answer and reasoning
8
Each of three positions has two choices, giving 2³=8.
CS / Foundations
Bits, bytes and representation
A bit has two possible values. Binary place values are powers of two, allowing bit patterns to represent numbers; character and image encodings assign other meanings to those patterns.
Learning objectives
- Explain bits, bytes and representation using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
A bit has two possible values. Binary place values are powers of two, allowing bit patterns to represent numbers; character and image encodings assign other meanings to those patterns.
Eight bits form a byte. A bit pattern has no unique meaning without its format: the same byte might represent an integer, a character code or part of a colour.
Equations and relationships
unsigned range with n bits = 0 to 2ⁿ−1
All bit patterns represent nonnegative values in this format.
Worked example
Convert binary 1101 to decimal.
Follow the solution
Use place values 8+4+0+1=13.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Use the prediction activity below; a local model appears only where it supports this topic.
Check your understanding
2. Convert binary 1101 to decimal.
- 13
- 11
- 1101
Check the answer and reasoning
13
Use place values 8+4+0+1=13.
3. Does one byte always mean one letter?
- Yes
- No
- Only on a phone
Check the answer and reasoning
No
Encodings differ; some characters require multiple bytes and some bytes are not text.