Floating Point Representation — A-Level Computer Science Revision
Revise Floating Point Representation 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 Number Systems & Binary ArithmeticWhat is Floating Point Representation?
Floating-point representation is a way of representing real numbers in a computer. It uses a formula to represent a number as a mantissa and an exponent. This allows for a wide range of numbers to be represented, including very small and very large numbers.
Board notes: Covered by AQA, Edexcel, and OCR. Students are expected to be able to convert between decimal and floating-point representation and to understand the concepts of mantissa, exponent, and normalization.
Step-by-step explanationWorked example
To represent 6.5 in floating-point, first convert to binary: 110.1. Normalize this to 1.101 x 2^2. The mantissa is 101 (the part after the point), and the exponent is 2. The sign is positive. These parts are then stored in the floating-point format.
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Common mistakes
- 1Making errors when converting decimal numbers to floating-point representation.
- 2Not understanding the concept of normalization.
- 3Confusing the mantissa and the exponent.
Floating Point Representation exam questions
Exam-style questions for Floating Point Representation 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 Floating Point Representation
Core concept
Floating-point representation is a way of representing real numbers in a computer. It uses a formula to represent a number as a mantissa and an exponent. This allows for a wide range of numbers to be …
Frequently asked questions
What are the limitations of floating-point representation?
Floating-point representation can lead to rounding errors and loss of precision. This is because not all decimal numbers can be represented exactly in binary. For example, 0.1 cannot be represented exactly in binary floating-point.
What is two's complement?
Two's complement is a way of representing negative numbers in binary. It is used in most computers because it simplifies arithmetic operations.