Bit flips amount to the heat dissipation in our microprocessors, leading to the

Question

Bit flips amount to the heat dissipation in our microprocessors, leading to the cost of heat sinking system to be installed in the CPU. In this exercise we quantify the magnitude of bit-flips as a function of stochastic input patterns.
Consider a fuller added circuit with inputs: (A, B and Cin) and outputs: Sum(S) and Carry (Cout). Suppose that during the execution of microprocessor ADD instruction, input are randomly and independently varying each with probability p.

randomly and independently varying each with probability p.
Calculate following probabilities:
a. Probability P(S) that output S is flipped when
i. ONE of randomly chosen inputs is flipped
ii. TWO of the randomly chosen inputs are flipped
iii. All THREE inputs are flipped
b. Probability P(Cout) that output Cout is flipped when
i. ONE of randomly chosen inputs is flipped
ii. TWO of the randomly chosen inputs are flipped
iii. All THREE inputs are flipped
c. Explain under which of the following circumstances are P(S) and P(Cout) mutually independent:
i. ONE of input bits flipped
ii. TWO of the input bits flipped
iii. All THREE of the input bits flipped
iv. Never

Explanation / Answer

a. Probability P(S) that output S is flipped when

ONE of randomly chosen inputs is flipped

b. Probability P(Cout) that output Cout is flipped when

ONE of randomly chosen inputs is flipped

c. Explain under which of the following circumstances are P(S) and P(Cout) mutually independent

Never

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