Computer Science A2 · Data Representation. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A real number is stored in two parts: a mantissa, which holds the digits, and an exponent, which says how many places to move the binary point. Value = mantissa × 2exponent. Both parts are in two's complement, and the binary point of the mantissa comes after its first bit.
A number is normalised when the first two bits of the mantissa are different. This gives one form for each value and the greatest precision for the bits available.
Only a limited set of values can be stored exactly. Many fractions, such as 0.1, have no exact binary form, so the stored value is an approximation and rounding errors appear in calculations.
Students read a negative mantissa as if it were positive. The first bit is worth −1, so 1.0100000 is −1 + 1/4 = −0.75, not 1.25 or −0.25.
Answer: −6 (the mantissa starts 10, so the number is normalised).
Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.
← File organisation and accessProtocols →Take a Computer Science A2 test