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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 following bit string of a number represented in BCD: 00000110. Give the integer number it represents.

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Given number -17, give the binary code to represent it in excess 30. Use 6 bits
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Give the upper limit of the range of values of integer representation two's complement with 7 bits? (highest integer value representable in decimal)

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Given the following bit string which represents an integer number in excess 34: 000011. Give the number it represents in decimal.

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Given a bit string which represents a real number in IEEE 754 single precicion:

SCCCCCCCCMMMMMMMMMMMMMMMMMMMMMMM

01111110110100000000000000000000

- Mantisa: Sign-Magnitud

S: Bit 31 -sign

M: Bits 22:0 - normalised mantissa (1.M with implicit 1 in the representation)

- Exponent: Excess 127

C: 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.

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Given a bit string which represents a real number in IEEE 754 single precicion:

SCCCCCCCCMMMMMMMMMMMMMMMMMMMMMMM

01111110110100000000000000000000

- Mantisa: Sign-Magnitud

S: Bit 31 -sign

M: Bits 22:0 - normalised mantissa (1.M with implicit 1 in the representation)

- Exponent: Excess 127

C: Bits 20:23 - 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.

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A number is represented in floating point according to the following format

S CCCC MMMMMM

1 0100 011100

- Mantisa: Sign-Magnitud

S: Bit 10 sign

M: Bits 5:0 - mantisa normalized as 1.M, so using an implicit 1

- Exponent: Exces 8

C: 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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