GCSE Computer Science Revision — Binary, Hex & Number Conversions
Revise Binary, Hex & Number Conversions for GCSE Computer Science with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
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What is Binary, Hex & Number Conversions?
At GCSE, you must be able to convert numbers between the denary (base-10), binary (base-2), and hexadecimal (base-16) number systems. Binary is the fundamental language of computers, while hexadecimal is often used as a more human-readable shorthand for binary, as one hex digit represents exactly four binary digits. Understanding these conversions is key to understanding how computers process and store numeric data.
Board notes: All boards (AQA, Edexcel, OCR) require you to be fluent in converting between denary, binary (up to 8 bits), and hexadecimal (up to 2 digits). Binary shifts are also a common topic on all specifications.
Step-by-step explanationWorked examples
Worked example
To convert the denary number 45 to binary: The largest power of 2 less than 45 is 32. 45 - 32 = 13. The largest power of 2 less than 13 is 8. 13 - 8 = 5. The largest power of 2 less than 5 is 4. 5 - 4 = 1. So, 45 = 32 + 8 + 4 + 1. In binary, this is 00101101 (using 8 bits). To convert this to hex, split it into two nibbles: 0010 and 1101. 0010 is 2. 1101 is 13, which is D in hex. So, 45 in denary is 2D in hexadecimal.
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Common mistakes
- 1Making place value errors when converting from binary or hex to denary. Remember binary place values are powers of 2 (1, 2, 4, 8, 16...) and hex are powers of 16.
- 2Forgetting that hexadecimal uses letters A-F to represent the denary values 10-15. A common mistake is to stop at 9.
- 3When converting from denary to binary, forgetting to write down a 0 in a place value column that isn't used. Every position must have a bit.
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Frequently asked questions
Why do we use hexadecimal in computer science?
Hexadecimal is used as a convenient, short-hand way to represent long binary numbers. Since one hex digit corresponds to a 4-bit binary number (a nibble), it makes it much easier for programmers to read and write binary values, such as memory addresses or colour codes.
How do you do a binary shift?
A logical binary left shift multiplies a number by 2 for each place shifted. A logical right shift divides it by 2. For example, shifting 000110 (6) one place to the left gives 001100 (12).