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CSCI 6307 Foundation of Systems – Exercise (2)

CSCI 6307 Foundation of Systems – Exercise (2). Xiang Lian The University of Texas – Pan American Edinburg, TX 78539 lianx@utpa.edu. Conversion Between Hexadecimal and Binary Numbers. Please convert the following hexadecimal numbers to binary numbers 2A (hex) E9 (hex) F100 (hex).

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CSCI 6307 Foundation of Systems – Exercise (2)

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

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

  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)

  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)

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

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

  7. Recall: IEEE Floating-Point Format single: 8 bitsdouble: 11 bits single: 23 bitsdouble: 52 bits S Exponent Fraction • 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? 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

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