Computer Organization and Structure
Homework
#3
Due:
2010/11/16
1. Given
the bit pattern:
1010
1101 0001 0000 0000 0000 0000 0010
what does
it represent, assuming that it is
a. A twofs
complement integer?
b. An
unsigned integer?
c. A
single precision floatingpoint number?
d. A
MIPS instruction?
2. We have
shown how to add and subtract binary and decimal numbers. However, other
numbering systems were also very popular when dealing with computers. Octal
(base 8) numbering system was one of these. The following table shows pairs of
octal numbers.

A 
B 
1 
5323 
2275 
2 
0147 
3257 
a. What
is the sum of A and B if they represent unsigned 12bit octal numbers? The
result should be written in octal. Show your work.
b. What
is the sum of A and B if they represent signed 12bit octal numbers stored in
signmagnitude format? The result should be written in octal. Show your work.
c. Convert
A into a decimal number, assuming it is unsigned. Repeat assuming it stored in
signmagnitude format. Show your work.
The
following table also shows pars of octal numbers.

A 
B 
1 
2762 
2032 
2 
2646 
1066 
d. What
is A  B if they represent unsigned 12bit octal numbers? The result should be
written in octal. Show your work.
e. What
is A  B if they represent signed 12bit octal numbers stored in signmagnitude
format? The result should be written in octal. Show your work.
f. Convert
A into a binary number. What makes base 8 (octal) an attractive numbering
system for representing values in computers.
3. A
majority function is generated in a combinational circuit when the output is
equal to 1 if the input variables have more 1fs than 0fs. The output is 0
otherwise.
a. Please
write the truth table for a 4input majority function.
b. Please
use the Karnaugh map to find the minimum sum of
products form and the minimum sum of products form for the complement.
c. Please
draw the logic schematic by using AND, OR, and INVERT gates.
4. The
ALU supported set on less than (slt) using just the
sign bit of the adder. Letfs try a set on less than operation using the values
7_{ten} and 6_{ten}. To make it simpler to follow the example,
letfs limit the binary representations to 4 bits: 1001_{two} and 0110_{two}.
1001_{two}
– 0110_{two} = 1001_{two} + 1010_{two} = 0011_{two}
This
result would suggest that 7_{ten} > 6_{ten}, which is
clearly wrong. Hence we must factor in overflow in the decision. Modify the
1bit ALU in the following figures to handle slt
correctly.
Figure
1: A 1bit ALU
that performs AND, OR, and addition on a and b or bf.
Figure
2: A 1bit ALU for
the most significant bit.