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CS230 Computer Organization

HomeWork #1 (Due: 1 week)

1. (1 Point) Suppose we want to store the decimal number -1000 at memory address 0x100 on a 32-bit computer.

a. Please first convert it to hexadecimal representation.

b. Please fill the converted hexadecimal representation in the memory.

2. (1 Point) Suppose we want to store the circumference ratio π in IEEE 754 single-precision representation.

a) What is the most precised value of π that can be represented by IEEE 754 single-precision? Please explain your method briefly.

b) Please convert the most precised value of π to IEEE 754 single-precision representation.

3. (1.5 Points) We are performing a 16-bit subtraction of Z = X - Y, where X = 4587. Suppose some pieces of information are known on the 16-bit fast adder’s top-level CLA74182 circuit, as annotated by the red numbers (P1=1, C2=0, C3=1, P4=0, and C4=1).

a) Please derive the possible values of Y, you should provide evidence for your answer.

b) Please give the possible results of Z, and whether overflow happens by using the signals in the circuit for your answer.

4. (1.5 Points) Complete the Booth Algorithm for Binary Multiplication for the following example, and fill in the 10-bit product.

Multiplicand: 13,  Multiplier: -9

Assume 5-bit multiplicand register, 5-bit ALU, and 10-bit Product register

The final 10-bit product (in binary) is:

The final 10-bit product (in decimal) is: