Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

  
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MULTIPLE CHOICE TEST

(All Tests)

FLOATING POINT REP

(More on Floating Point Representation)

INTRO TO SCIENTIFIC COMPUTING

(More on Scientific Computing)

Pick the most appropriate answer.

Q1. A hypothetical computer stores real numbers in floating point format in 8-bit words.  The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next two bits for the magnitude of the exponent, and the next four bits for the magnitude of the mantissa.  Represent e≈2.718 in the 8-bit format.

  00010101

  00011010

  00010011

  00101010

 

Q2. A hypothetical computer stores real numbers in floating point format in 8-bit words.  The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next two bits for the magnitude of the exponent, and the next four bits for the magnitude of the mantissa.  The base-10 number that (10100111)2 represents in the above given 8-bit format is

  -5.75000

  -2.87500
  -1.75000
  -0.359375

 

Q3. A hypothetical computer stores floating point numbers in 8-bit words.  The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next two bits for the magnitude of the exponent, and the next four bits for the magnitude of the mantissa.  The machine epsilon is most nearly

  2-7
  2-4

  2-3 

  2-2

 

Q4. A machine stores floating point numbers in 7-bit word.  The first bit is used for the sign of the number, the next three for the biased exponent and the next three for the magnitude of the mantissa.  The number (0010110)2 represented in base-10 is

  0.375

  0.875

  1.5

  3.5


Q5. A machine stores floating point numbers in 7-bit words.  The first bit is stored for the sign of the number, the next three for the biased exponent and the next three for the magnitude of the mantissa.  You are asked to represent 33.35 in the above word.  The error you will get in this case would be

  underflow
  overflow

  NaN

  No error will be registered

 

Q6. A hypothetical computer stores floating point numbers in 9-bit words.  The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next three bits for the magnitude of the exponent, and the next four bits for the magnitude of the mantissa.  Every second, the error between 0.1 and its binary representation in the 9-bit word is accumulated.  The accumulated error after one day most nearly is

  0.002344
  20.25
  202.5

  8640

  

 

Complete solution 

 

             

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

  

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