Learning objective
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.
Read the explanation, check the common trap, then practise with flashcards and questions.
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Binary number system
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Unsigned binary
Aqa A Level Computer ScienceFundamentals of data representation
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Quick explanation
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
- This point belongs to Binary number system, especially Unsigned binary.
- You need to be able to 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.
- 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 Unsigned binary to exam-style questions, flashcards, and revision notes for Binary number system.
Quick student answer
What is the decimal value of the unsigned binary number 101101?
Direct answer
45
Key terms
- Unsigned binary: A binary number system that represents only non-negative values, from 0 up to a maximum determined by the number of bits.
- Bit: A binary digit that can have a value of 0 or 1 and contributes a place value when it is 1.
Common trap
Using the wrong maximum-value formula: Use 2^n - 1. There are 2^n possible bit patterns, but the values start at 0, so the largest value is one less than 2^n.
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Related learning objectives
- 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
- Absolute and relative errors: Be able to calculate the absolute error of numerical data stored and processed in computer systems. Be able to calculate the relative error of numerical data stored and processed in computer systems. Compare absolute and relative errors for large and small magnitude numbers, and numbers close to one.
Absolute and relative errors