Number Systems & Binary Arithmetic — A-Level Computer Science Revision
Revise Number Systems & Binary Arithmetic for A-Level Computer Science. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Character EncodingWhat is Number Systems & Binary Arithmetic?
Number systems are the different ways of representing numbers. The most common are decimal (base 10), binary (base 2), and hexadecimal (base 16). Binary arithmetic is the process of performing arithmetic operations (addition, subtraction, multiplication) on binary numbers.
Board notes: A fundamental topic for AQA, Edexcel, and OCR. Students must be proficient in converting between number systems and performing binary arithmetic.
Step-by-step explanationWorked example
To add the binary numbers 1011 and 0110: \n` 1011` \n`+ 0110` \n`-----` \n` 10001` \nStarting from the right, 1+0=1. 1+1=10 (0, carry 1). 1+0+1=10 (0, carry 1). 1+1=10 (0, carry 1). The result is 10001.
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Common mistakes
- 1Making errors in binary addition, especially with carrying over.
- 2Confusing hexadecimal digits (A-F) with letters.
- 3Incorrectly converting between number systems, particularly with fractional numbers.
Number Systems & Binary Arithmetic exam questions
Exam-style questions for Number Systems & Binary Arithmetic with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel and OCR specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Number Systems & Binary Arithmetic
Core concept
Number systems are the different ways of representing numbers. The most common are decimal (base 10), binary (base 2), and hexadecimal (base 16). Binary arithmetic is the process of performing arithme…
Frequently asked questions
Why do computers use binary?
Computers use binary because it is a reliable way to represent the two states of electronic circuits: on and off (or high and low voltage). These two states can be represented by the digits 1 and 0.
What is hexadecimal used for?
Hexadecimal is often used in computing as a more human-readable representation of binary data. Each hexadecimal digit corresponds to a group of four binary digits, making it easier to read and write long binary numbers.