Reference no: EM133522409
Computer Architecture
Question 1
Consider the problem of overflow detection from a 32-bit signed add/subtract unit. The available inputs are: a31-a0 (the 32 bits of the "a" operand; with a31 being the most significant bit and a0 being least significant bit), b31-b0 (same for the "b" operand), r31- r0 (the 32 bits of the result), and "S" an input where 0 means perform addition (a+b) and 1 means perform subtraction (a - b).
(a) Write the Truth Table for the Overflow output bit.
Hint: You should use 4 input bits: a31, b31, r31, and S.
(b) Write a sum-of-products or product-of-sums Boolean function for Overflow.
(c) Draw a logic circuit that implements the Boolean function from (b) using only AND and OR gates with inverters on complemented inputs.
(d) What is the size of your circuit in gates? Only count AND and OR gates.
(e) What is the gate delay of your circuit? Consider each AND/OR gate as a delay of 1, i.e., ignore delays caused by inverters or wires.
Question 2
Suppose an improvement on a given program is proposed for an architecture with Speedup=30. What fraction of the time must the improvement be used to achieve an overall speedup of 10 for the entire program? Hint: You should apply Amdahl's Law.
Question 3
Consider adding a register-memory addressing mode for source operands of ALU instructions to a load-store machine. The idea is to replace sequences of
LOAD R1, 0(Rb) # R1 = MEM[0 + Rb]
ADD R2, R1, R2 # R2 = R1 + R2
by the single instruction
ADD R2, 0(Rb) # R2 = R2 + MEM[0+Rb]
Assume that the new instruction will cause the clock cycle of the processor to increase by 5%. Answer the following using the instruction mix:
40% ALU, 25% Jumps, 20% Load, 10% Store, 5% Other Also assume that every instruction has the same CPI (e.g., 1.0).
(a) What percentage of loads must be eliminated for the machine with the new instruction to have at least the same performance as original?
Hint: use the Iron Law.
(b) Can this replacement be applied for all sequences of load followed by an ALU operation of the loaded value, or is there a situation where this cannot be used?
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