# CZ1101, Tutorial 5, 6-11 October, 1997

Do the problems before going to the tutorial class. You need not hand in the solutions.

1. (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?
2. (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.
3. [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.
4. [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?
5. (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.
6. (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)].
7. (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).