Topic 1: Binary, Decimal Conversion
Computers use binary (base-2) numbers, made of 0s and 1s, and we can convert between binary and decimal (base-10) numbers we normally use.
Core concept
Binary numbers use only two digits, 0 and 1, with each position representing a power of 2 (1, 2, 4, 8, 16, and so on).
How it works
To convert binary to decimal, we multiply each digit by its place value (power of 2) and add the results together.
Why it matters
For example, binary 101 converts to decimal: (1×4) + (0×2) + (1×1) = 4+0+1 = 5.
Key detail
To convert decimal to binary, we repeatedly divide by 2 and track the remainders, then read them in reverse order.
Exam highlight
Key diagram

- A place-value chart showing powers of 2 (1,2,4,8,16...) used to convert a decimal number to binary.
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Quick notes
• Binary numbers use only 0 and 1.
• Each position represents a power of 2.
• Convert binary to decimal by multiplying and adding place values.
• Binary 101 = (1×4)+(0×2)+(1×1) = 5.
• Convert decimal to binary by dividing by 2 repeatedly.
• Track remainders and read in reverse.
• Computers use binary internally.
• Conversion connects human and computer number systems.