Foundations · StudentHub Lesson
Binary & Number Systems
Discover how computers represent numbers, letters, and data using binary digits.
What you will learn
- Convert between binary and decimal numbers
- Explain why computers use base-2
- Understand bits and bytes
- Represent letters using binary codes
- Recognize hexadecimal as a shorthand for binary
Watch the lesson
Representing Numbers and Letters with Binary: Crash Course Computer Science #4 · CrashCourse
Watch on YouTubeTopic notes
Main Idea
Computers represent all data—numbers, letters, images—using binary (base-2) digits, because transistors only have two states.
Key Concepts
- Binary uses only 0s and 1s
- Each binary digit is called a bit; 8 bits make a byte
- Binary numbers can represent decimal numbers using powers of 2
- Letters are represented using codes like ASCII
Definitions
- Bit: a single binary digit (0 or 1)
- Byte: a group of 8 bits
- ASCII: a standard that maps letters to binary numbers
Syntax / Conversion
```
Binary 101 = 14 + 02 + 1*1 = 5 (decimal)
```
Examples
- Decimal 5 in binary is 101
- The letter 'A' in ASCII is 65, or 01000001 in binary
Common Mistakes
- Reading binary digits in the wrong order (place values)
- Confusing bits with bytes
Key concepts
Important terms
- Bit
- A single binary digit, either 0 or 1
- Byte
- A group of 8 bits
- ASCII
- A character encoding standard mapping letters to numbers
Worked examples
Problem
Convert binary 1010 to decimal
- 1. 1*8 + 0*4 + 1*2 + 0*1
- 2. = 8 + 0 + 2 + 0
Answer: 10
Quick revision
- Binary uses only 0 and 1
- 8 bits = 1 byte
- Place values double as you move left
- ASCII encodes letters as numbers
- Computers use binary because transistors have two states
Check your understanding
Question 1 · Multiple choice
How many bits are in a byte?
Question 2 · Multiple choice
What is the decimal value of binary 101?
Question 3 · True or false
Computers use base-10 numbers internally.
Question 4 · Short answer
What does ASCII do?
Question 5 · Short answer
Convert decimal 6 to binary.
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