Sala común de la asignatura Tecnología de Computadores. Plan 2023 (2024-25, Grado en Ing del Software, Informática, de Computadores y Doble Grado Matemáticas + Informática, Todos los grupos)
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Given the single precision IEEE 754 representation:
SCCCCCCCCMMMMMMMMMMMMMMMMMMMMMMM
00111110011100000000000000000000- Mantisa: Signed-MagnitudS: Bit 31 -signM: Bits 30:23 - fractional normalized mantisa (1.M with implicit 1)- Exponent: Excess 127C: Bits 22:0 - characeristic representing the exponent in excess 127The represented value is given by = (-1)S x 1.M x 2C-127 as long as we are not dealing with a special case.
Determine the represented number in decimal notation. In the nswer, consider only 5 significative digits, i.e. digits that differ from 0.
Given a bit string which represents a real number in IEEE 754 single precicion:
SCCCCCCCCMMMMMMMMMMMMMMMMMMMMMMM
11000000011100000000000000000000- Mantisa: Sign-Magnitud S: Bit 31 -signM: Bits 22:0 - normalised mantissa (1.M with implicit 1 in the representation)- Exponent: Excess 127C: Bits 30:23 - characteristic (exponent represented in excess 127)The represented value is given by V = (-1)S x 1.M x 2C-127 if it is not a special case.
Determine the represented real value in decimal with at most 5 significative digits (different from 0). For instance use decimal notation with a decimal comma, e.g. -2,625 or you can also use the scientific notation, e.g. -5,5432e-23.
A number is represented in floating point according to the following format
S CCCC MMMMMM1 1100 010101- Mantisa: Sign-MagnitudS: Bit 10 signM: Bits 5:0 - mantisa normalized as 1.M, so using an implicit 1 - Exponent: Exces 8C: Bits 9:6 - characteristic for the exponent in exces 8)
So the represented number is V = (-1)S x 1.M x 2C-8
Give the represented number in decimal considering only 5 significative digits (nonzero) Example 1.2345
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