1. CSCI 6307 Foundation of Systems – Exercise (2) Xiang Lian The University of Texas – Pan American Edinburg, TX 78539 lianx@utpa.edu 1

2. Conversion Between Hexadecimal and Binary Numbers Please convert the following hexadecimal numbers to binary numbers – 2A (hex) – E9 (hex) – F100 (hex) 2

3. Conversion Between Hexadecimal and Binary Numbers (cont'd) Please convert the following binary numbers (2's complement) to hexadecimal numbers – 0001 0100 1111 1001 (2) – 1000 1011 0100 1010 (2) 3

4. Arithmetic Operations Please use 4 bits to perform arithmetic operations in binary representations, and tell whether there is any overflow – 1000 (2) + 0111 (2) – 1001 (2) + 1011 (2) – 0111 (2) + 0101 (2) – 0110 (2) + 0110 (2) – 7 (10) + 7 (10) 4

5. Conversion from Decimal Numbers to Binary Numbers Please convert the following decimal numbers to binary numbers – 12.5 – 30.2 – 8.75 5

6. Floating Point Representation Please give the binary representation of the floating point number, 12.5, assuming the IEEE 754 single precision format 6

7. Recall: IEEE Floating-Point Format 7 SExponentFraction single: 8 bits double: 11 bits single: 23 bits double: 52 bits S: sign bit (0  non-negative, 1  negative) Normalize significand: 1.0 ≤ |significand| < 2.0 – Always has a leading pre-binary-point 1 bit, so no need to represent it explicitly (hidden bit) – Significand is Fraction with the “1.” restored Exponent: excess representation: actual exponent + Bias – Ensures exponent is unsigned – Single: Bias = 127; Double: Bias = 1203

8. What is the clock cycle time of the datapath, if we only need to support ALU instructions? 8 I-Mem: 200ps Add: 70ps Mux: 20ps ALU: 90ps Regs: 90ps D-Mem: 250ps Sign-Extend: 15ps Control: 10ps

9. Classifications and Terminologies List the 2 types of elements in the logic design. Give an example for each type. List 5 stages of the instruction execution in the pipeline What is the maximum speedup when considering the pipeline? List 3 types of situations/hazards that cause bubbles in the pipeline 9