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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 simple precision IEEE 754 representation:
- 32 bits.
- Mantisa of 24 bits, fixed point (sign in bit 31, magnitud in bits 22:0) with 1 implícit.
- Characteristic of 8 bits (bits 30:23) represents the exponent in excess 127.
- Binary string: SCCCCCCCCMMMMMMMMMMMMMMMMMMMMMMM
represent real number 1,4 in this format
Given the single precision IEEE 754 representation:
SCCCCCCCCMMMMMMMMMMMMMMMMMMMMMMM
11000001111100000000000000000000- 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.
Give the upper limit of the range of values of integer representation two's complement with 4 bits? (highest integer value representable in decimal)