PS2s - Department of Electrical and Computer Engineering...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Department of Electrical and Computer Engineering McGill University ECSE-322 Computer Engineering Fall 2010 Problem Set 2 - Solutions 1. Floating point representation: (a) Show the IEEE-754 binary representation of the number –0.75 (i.e.- ¾ in base 10) using the single precision format. Solution: For IEEE, bit 31 is the sign but, bits 30-23 are the exponent bits and are stored in excess-127, and the rest are for the mantissa using hidden bit normalization. -0.75 = -3/4 = -3 * 2 -2 = -1.5 *2 -1 The resultant representation is: 10111111010000000000000000000000, where the sign=-1, the exponent=-1 and the mantissa=1.5 (b) What floating point number (in IEEE-754 format) is represented by the following: 00110000001000000000000000000000 Solution: 00110000001000000000000000000000 = -1 0 x 2 (96-127) x (1 + 2 -2 ) = 5.820766x10 -10 (c) Represent 0.125 16 5 and -0.125 x 16 -5 in USASI. Solution: Recall that, for USASI, bit 0 = sign bit bits 1-7 = exponent bits stored in excess-64 bits 8-31 mantissa bits (six hexadecimal digits normalized fraction)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The exponent 5 in excess 64 is equal to 69 (1000101) The mantissa 0.125 is 1/8 = 2/16 = 2*16 -1 , thus 0.2 in hexadecimal (hence 0100 …) The exponent –5 in excess 64 is equal to 59. Thus resulting representation follows: 0.125 x 16 5 is represented as 0 1000101 0010 0000 0000 0000 0000 0000 -0.125 x 16 -5 is represented as 1 0111011 0010 0000 0000 0000 0000 0000 (d) Identify how infinity, not a number, and 0 are represented in IEEE-754 and USASI. Solution: IEEE-754: Infinity: all exponent values are =1, all mantissa values are = 0. NaN : all exponent values are = 1, mantissa = non zero 0: all bits are = 0 USASI: Cannot represent infinity or NAN 0: Mantissa bits are 0 2. Determine the maximum relative error and minimum and maximum values of a real number
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/22/2010 for the course ECSE ECSE 322 taught by Professor Lowther during the Winter '04 term at McGill.

Page1 / 5

PS2s - Department of Electrical and Computer Engineering...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online