Do the problems before going to the tutorial class.
You need not hand in the solutions.
(4.11-4.13) [15] What are the IEEE single precision
representations for the numbers 10.0, 10.5, and 0.1? (Give the
32-bit patterns for the numbers). What are the IEEE double
precision representations for the same set of numbers?
(4.41) [5] Add 6.42_ten x 10^1 to
9.51_ten x 10^2 in decimal notation, assuming
that you have only three significant digits, first with
guard and round digits and then without them.
[15] Multiply 8.76_ten x 10^1
to 1.47_ten x 10^2. This time, in binary
floating point with 4 bits of significand. You need to
find the binary representations first.
[15] For arithmetic done in IEEE single-precision
floating point format (with guard and round bits),
give a positive number x that when added to 1.0
produces the result x. That is, give a value for x such
that x>0 and x+1.0 = x. What is the smallest number x
that satisfies the condition? What if the computation is in
double precision?
(4.22) [10] Find the shortest sequence of MIPS
instructions to determine if there is a carry out from
the addition of two registers, say register $11 and $12.
Place a 0 or 1 in register $10 if carry out is 0 or 1,
respectively.
(4.23) [15] Find the shortest sequence of MIPS instructions
to perform double precision integer addition. Assume that
one 64-bit two's complement integer is in register
$12 and $13 and another is in registers $14 and $15.
The sum is to be placed in registers $10 and $11. In this
example the most significant word of the 64-bit integer
is found in the even-numbered registers, and the least
significant word is found in the odd-numbered registers.
[You need answer to (4.22)].
(4.24) [20] Find the shortest sequence of MIPS instructions
to perform double precision integer multiplication. Assume that
one 64-bit, unsigned integer is in registers $12 and $13
and another is in registers $14 and $15. The 128-bit product
is to be placed in registers $8, $9, $10, and $11. The most
significant word is found in the lower numbered registers, and the
least significant word is found in the higher numbered registers in
this example. Hint: Write out the formula for (a 2^{32} + b) x
( c 2^{32} + d).