CSCI 463 Spring 2018

Name ________________            Z-Id _________________

Questions on front and back.

Using the last digit of your Z-ID, select the value you will be using for
question 1.  On the test there will be 10 values.

1) 1993      2)  1776       3) 1883      4) 999       5) 1111

6) 2001      7)  1987       8) 2008      9) 765       0) 8383

Convert an decimal integer to its binary. You must show work to get points.

1. Using 12 bit storage, Show work on blank sheets

a.(2) Convert value to binary (use divide by 2 (shift right) ).






b.(2) Convert value to binary (use subtract powers of 2 ).





c.(1) Give hex representation.


d.(1) Give octal representation.



e.(2) Give 2's complement binary, remember we are using a 12 bit word.


f.(2) Convert 12 bit 2's complement back as an unsigned decimal value,
  Use multiply by 2 and add method.

2.(2) Give the generic formula for calculating the bias value.

Using the last digit of your Z-ID, select the value you will be using for
question 3.  On the test there will be 10 values.

3. Floating point numbers :  number from table convert to a float that uses a
n-bit significand, an m-bit exponent and a sign bit. You must show work to get
points.

The following table consists of value to convert, the exponent size, and the
signifiand size, example  -100.1,14,7  -100.1 is the float, use a 14 bit
exponent, and a 7-bit significand.

Examples of possible values.

77.69, 11, 8
-111.67, 10, 8
-123.321, 8, 9
232.323, 7, 9
199.77, 11, 10
-444.46, 9, 10
501.88, 8, 11
-678.90, 12, 11
888.77, 9, 12
987.65, 6, 12

a.(2) Convert the integer portion to binary, your choice of manual calculation.













b.(2) Use shift left (multiply by 2) method to convert fractional portion to
binary. You man trucate when sufficient number of bits caculated.












c.(2) Show number in binary hybrid form of scientific notation 1.bbbbbbb x 2^y



d.(2) Calculate the final biased exponent.






e.(3) Show the completed binary floating point number as it will be stored.

Name ________________            Z-Id _________________

4. Use the 2nd to last digit of your Z-ID to select the stored float from the
table below. Convert value below back to decimal. Show work to get full or
partial credit. Values are listed as stored float, size of exponent field, and
size of significand field.

01000010111010111, 8, 8
1100010010111001, 7, 8

0100111001100110, 6, 9
1100110000100101, 6, 9

01000001011100001010, 9, 10
10111111101000000000, 9, 10

001110111000000000, 8, 9
11000110010101010, 7, 9

10000011010110011, 9, 7

* Copy your answer from  3.e.   ____________________________

a.(1) Calculate the bias.




b.(2) Extract the biased exponent and unbias.






c.(2) Extract the significand and using the unbiased exponent, show the binary
float with the decimal point in the appropriate place.



d.(1) Convert the integer portion of the value to decimal. Use preferred method
but show work.







d.(1) Convert the fractional portion of the value to decimal. Use preferred method
but show work.




e.(1) Put the parts together, remember to use the appropriate sign.




5.(9) Float - min and max,  format is 5 bit mantissa and 6 bit exponent.

 a.(1) Show binary representation of the largest normalized that can be represented.



 b.(2) What is the actual value? ( Put it in the form of 2^x-2^y)



 c.(1) Show binary representation of smallest NORMALIZED value that can be represented.



 d.(2) What is the actual value? ( Put it in the form 1.0 x 2^Y )



 e.(1) Show binary representation of smallest DENORMALIZED value that can be represented.



 f.(2) What is the actual value? ( Put it in the form 1.0 x 2^Y )
6.(10) T/F  True/False - make sure I can tell the difference between T and F

___  A byte is/was always 8 bits.


___  A word is determined by the particular system's architecture.


___  ASCII is an 8-bit character code.


___  EBCDIC is an 8-bit character code.


___  Unicode is an 8-bit character code.


___  UCS-16 is a fixed 2 byte character set.


___  The Unicode Glyph aspect determines the meaning of the character.


___  The Unicode Grapheme aspect determines the meaning of the character.


___  The Unicode Rules aspect determines the meaning of the character.


___  UTF-8 is dominant version for World-wide web.


___  UTF-16 is dominant version for World-wide web.


___  UCS-4 is a 2 or 4 byte variable length Unicode format.


___  Universal Coded Character Set (UCS) standard evolved from Unicode.


___  Universal Coded Character Set (UCS) standard does not cover rules such as
collating or paired character exceptions.


Name ________________            Z-Id _________________


7.(8) Using booth's algorithm, multiply the two 8-bit values provided. Use the
algorithm exampled on the Wikipedia article and my lecture page. The final
value will be a 16-bit signed number. You may leave it in binary.

1) -121,14   2)  87,93     3) 111,-111   4) 84,-93    5) -55,56

6) 23,-123   7)  -43,-55   8) 88,66      9) 86,-88    0) 104,29