In simple terms
A friendly intro before the formal notes — no formulas yet.
Flipping the Switches
Computers represent all information using binary, a system of only 0s and 1s. This is like a huge bank of light switches, where each switch is either off (0) or on (1), and patterns of these switches represent numbers, letters, and colours.
Imagine you need to count items but you can only use your hands. You could raise a finger for each item, but you'd run out at ten. A more efficient system is to assign a value to each finger: your thumb is 1, index finger is 2, middle finger is 4, ring finger is 8, and little finger is 16. By raising combinations of fingers (e.g., index and thumb for '3'), you can represent any number up to 31 on one hand. Binary works exactly like this, but with 'on' (1) and 'off' (0) states instead of raised or lowered fingers.
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First, understand that our normal numbers are 'denary' or 'base-10', with place values like 1, 10, 100 (powers of 10).
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Binary is 'base-2'. Its place values are powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, and so on, from right to left.
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To convert a denary number to binary, find the largest power of 2 that fits inside it, place a '1' in that position, subtract it, and repeat with the remainder.
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To convert a binary number to denary, simply add up the place values for every position that contains a '1'.
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Full topic notes
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Understanding Number Systems
We are accustomed to the denary (or base-10) number system, which uses ten digits (0-9). The position of a digit determines its value based on powers of 10. For example, the number 345 is really . Computers use the binary (or base-2) system, which works on the same principle but with only two digits (0 and 1) and place values based on powers of 2.
Binary Place Values (right to left): Which are:
Converting Between Denary and Binary
Being able to convert numbers between denary and binary is a crucial skill. To convert from denary to binary, you can use the subtraction method. To convert from binary to denary, you sum the place values of all positions that hold a '1'.
Representing Other Data
Binary isn't just for numbers. Every piece of data is stored as a binary pattern. For text, computers use character sets like ASCII or Unicode, which are essentially dictionaries that map each character (like 'A', 'b', or '£') to a unique binary number. For example, in ASCII, the capital letter 'A' is represented by the denary number 65, which is in binary.
All data in a computer is stored in binary (base-2).
A bit is a single 0 or 1; a byte is a group of 8 bits.
An 8-bit byte can represent any integer from 0 to 255.
Conversion from denary to binary often uses repeated subtraction from the largest place value.
Conversion from binary to denary involves summing the place values where a '1' is present.
Character sets like ASCII and Unicode map characters to specific binary codes.
Worked examples
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Convert the denary number into an 8-bit binary integer. Show your working.
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Is ? Yes. Place a '1'. Remainder: .
Convert the 8-bit binary number into its denary equivalent. Show your working.
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We write down the binary number and the corresponding place values for each bit. Then, we sum the place values where the bit is '1'.
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What is a 'bit'?
The smallest unit of data in a computer, representing a single binary value of either 0 or 1. Short for 'binary digit'.
Key takeaways
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All data in a computer is stored in binary (base-2).
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A bit is a single 0 or 1; a byte is a group of 8 bits.
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An 8-bit byte can represent any integer from 0 to 255.
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Conversion from denary to binary often uses repeated subtraction from the largest place value.
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Conversion from binary to denary involves summing the place values where a '1' is present.
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Character sets like ASCII and Unicode map characters to specific binary codes.
Practice — then mark it
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Test Your Knowledge on Binary Representation
Test Your Knowledge on Binary Representation
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