**Computer Organization and Structure**

Homework
#3

Due:
2008/11/4

1. The
ALU supported set on less than (slt)
using just the sign bit of the adder. Let’s try a set on less than
operation using the values -7_{ten} and 6_{ten}. To make it
simpler to follow the example, let’s 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 1-bit
ALU in the following figures to handle slt correctly.

Figure
1: A 1-bit ALU
that performs AND, OR, and addition on a and b or b’.

Figure
2: A 1-bit ALU for
the most significant bit.

2. Given
the bit pattern:

1010
1101 0001 0000 0000 0000 0000 0010

what
does it represent, assuming that it is

a.
a two’s complement integer?

b.
an unsigned integer?

c.
a single precision floating-point
number?

d.
a MIPS instruction?

3. Add
2.85_{ten} x 10^{3} to 9.84_{ten} x 10^{4} and
add 3.63_{ten} x 10^{4} to 6.87_{ten} x 10^{3},
respectively, assuming that you have only three significant digits, first with
guard and round digits and then without them.

4. Consider
two different implementations, I1 and I2, of the same instruction set. There
are three classes of instructions (A, B, and C) in the instruction set. I1 has
a clock rate of 6GHz, and I2 has a clock rate of 3GHz. The average number of
cycles for each instruction class on I1 and I2 is given in the following table:

Class |
CPI
on M1 |
CPI
on M2 |
C1
Usage |
C2
Usage |
C3
Usage |

A |
2 |
1 |
40% |
40% |
50% |

B |
3 |
2 |
40% |
20% |
25% |

C |
5 |
2 |
20% |
40% |
25% |

The
table also contains a summary of average proportion of instruction classes
generated by three different compilers. C1 is a compiler produced by the makers
of I1, C2 is produced by the makers of I2, and the other compiler is a
third-party product. Assume that each compiler uses the same number of
instructions for a given program but that the instruction mix is as described
in the above table. Using C1 on both I1 and I2, how much faster can the makers
of I1 claim I1 is compared to I2? Using C2, how much faster can the makers of
I2 claim that I2 is compared to I1? If you purchase I1, which compiler would
you use? If you purchased I2, which compiler would you use? Which computer and
compiler would you purchase if all other criteria are identical, including
cost?