Fordham, New York City's Jesuit University
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FORDHAM UNIVERSITY CISC 3593
Fordham College Lincoln Center Computer Organization
Dept. of Computer and Info. Science Spring, 2011



Homework Assignment 5
Due date: March 8

Note: most these have been altered considerably from the correspondingly numbered text questions.


Exercise 2.7

The following problems explore number conversions from signed and unsigned binary numbers to decimal numbers. Show all work. You may use a calculator, but not one that converts for you (except to check your work).

a. 0101 1100 ${}_{\mbox{\tt\scriptsize two}}$

b. 1111 1001 ${}_{\mbox{\tt\scriptsize two}}$

c. 0010 1101 0001 0010 ${}_{\mbox{\tt\scriptsize two}}$

d. 1011 0011 0101 0011 ${}_{\mbox{\tt\scriptsize two}}$

2.7.1
[10 pts.] <§2.4>For the bit patterns above, what base 10 number does each represent, assuming that it is a two's complement integer (i.e. an integer expressed using the two's complement representation)?

2.7.2
[10 pts.] <§2.4>For the bit patterns above, what base 10 number does each represent, assuming that it is an unsigned integer?

2.7.3
[10 pts.] <§2.4>For each bit pattern above, what hexadecimal number does it represent?

2.7.3a
[5 pts.] <§2.4>Sign-extend each of the 8-bit patterns in a and b above to 16-bit patterns, so that they continue to represent the same respective values when interpreted as two's complement integers.

The following problems explore number conversions from decimal to signed and unsigned binary numbers. Show all work.

a. 24 ${}_{\mbox{\tt\scriptsize ten}}$

b. 109 ${}_{\mbox{\tt\scriptsize ten}}$

c. 1 000 ${}_{\mbox{\tt\scriptsize ten}}$

d. 27 483 ${}_{\mbox{\tt\scriptsize ten}}$

2.7.4
[10 pts.] <§2.4>For each of the base ten numbers above, convert to binary using the two's complement representation. For a and b, express the results using an 8-bit word size; for c and d, use a 16-bit word size.

2.7.6
[10 pts.] <§2.4>Express the negative of each of the base ten numbers above in binary using two's complement representation. For a and b, express the results using an 8-bit word size; for c and d, use a 16-bit word size.

Exercise 2.10

In the following problems, the bit patterns represent MIPS instructions. You will be asked to translate the entries into assembly code and determine what format of MIPS instruction the bits represent.

a. 1010 1110 0000 1011 0000 0000 0000 0100 ${}_{\mbox{\tt\scriptsize two}}$

b. 1000 1101 0000 1000 0000 0000 0100 0000 ${}_{\mbox{\tt\scriptsize two}}$

c. 0000 0010 0001 0001 1100 0000 0010 0000 ${}_{\mbox{\tt\scriptsize two}}$

d. 0010 0010 0001 0001 0000 0000 0010 0100 ${}_{\mbox{\tt\scriptsize two}}$

2.10.1
[10 pts.] <§2.5>For each of the binary bit patterns above, what instruction does it represent? Express in standard assembly notation using register names such as $t0 etc., not numbers.

2.10.2
[5 pts.] <§2.5>What type (I or R) of instruction format does each of the binary bit patterns above represent?

2.10.3
[5 pts.] <§§2.4, 2.5>Express each of the binary instructions above in hexadecimal.


Robert Moniot 2011-03-07