Learning objective
Underflow and overflow: Explain underflow and overflow and describe the circumstances in which they occur.
Read the explanation, check the common trap, then practise with flashcards and questions.
At a glance
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Topic
Binary number system
Subtopic
Underflow and overflow
Study support
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Quick explanation
Underflow and overflow: Explain underflow and overflow and describe the circumstances in which they occur
- This point belongs to Binary number system, especially Underflow and overflow.
- You need to be able to underflow and overflow: Explain underflow and overflow and describe the circumstances in which they occur.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Why it matters
This objective helps connect Underflow and overflow to exam-style questions, flashcards, and revision notes for Binary number system.
Quick student answer
What is overflow in a fixed-size binary number system?
Direct answer
The result is too large to be represented using the available number of bits
Key terms
- Overflow: The condition in which a calculation produces a value greater than the maximum value representable using the available fixed number of bits.
- Underflow: The condition in which a calculation produces a value less than the minimum value representable using the available fixed number of bits.
Common trap
Reversing the two conditions: Remember that overflow is above the maximum representable value, while underflow is below the minimum representable value.
Related questions
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Related learning objectives
- Unsigned binary: Know the difference between unsigned binary and signed binary. Students are expected to be able to convert between unsigned binary and decimal and vice versa. Know that in unsigned binary the minimum and maximum values for a given number of bits, n, are 0 and 2n -1 respectively.
Unsigned binary
- Unsigned binary arithmetic: Be able to: • add two unsigned binary integers • multiply two unsigned binary integers. 66
Unsigned binary arithmetic
- Signed binary using two’s complement: Know that signed binary can be used to represent negative integers and that one possible coding scheme is two’s complement. This is the only representation of negative integers that will be examined. Students are expected to be able to convert between signed binary and decimal and vice versa. Know how to: • represent negative and positive integers in two’s complement • perform subtraction using two’s complement • calculate the range of a given number of bits, n.
Signed binary using two’s complement
- Numbers with a fractional part: Know how numbers with a fractional part can be represented in: • fixed point form in binary in a given number of bits • floating point form in binary in a given number of bits. Students are not required to know the Institute of Electrical and Electronic Engineers (IEEE) standard, only to know, understand and be able to use a simplified floating representation consisting of mantissa + exponent. Be able to convert for each representation from: • decimal to binary of a given number of bits • binary to decimal of a given number of bits. Exam questions on floating point numbers will use a format in which both the mantissa and exponent are represented using two's complement.
Numbers with a fractional part
- Rounding errors: Know and be able to explain why both fixed point and floating point representation of decimal numbers may be inaccurate. Use binary fractions. For a real number to be represented exactly by the binary number system, it must be capable of being represented by a binary fraction in the given number of bits. Some values cannot ever be represented exactly, for example 0.110.
Rounding errors