Day 8

Question 1

What is a transparent latch? why is it important?

Answer 1

• Transparent latch is a latch where the input is passed straight to the output once the “enable” is set. That is, we have control on when is gets its input.
• It is important when we can technically execute a couple of instructions per one clock cycle(in terms of buses) but the order of them matters.

Question 2

Recall

Answer 2

Question 3

• What causes a great delay using ripple carry adders?*
• How can it be fixed?*

Answer 3

* Each adder block waits for the carry to arrive from its previous block.

• We want to remove the sequential order of the ripple carry adders.
  
  • Define: Gi = Ai*Bi
  • Define: Pi = Ai XOR Bi
  • Ci+1 = Gi + Pi*Ci

What we formed here is a recursive formula, such that Ci depends on Cin, Gi’s and Pi’s. Gi’s and Pi’s can be computed independely of each other, thus the computation can occur simultaneously.

Question 4

What is the formula for determining the time it takes to compute addition between two numbers of n bits, with level k?

From which n does it satisfies better timing than ripple carry adder?

Answer 4

1+ 4log^n(base k)

for n = 5.

Question 5

Recall

Answer 5

Question 6

Recall the answer for this analysis

Answer 6

First build the tree of Ci’s for k=2.

Second, recall that computing Ci+1 once you have cj and all of its coefficients(P’s and G’s), takes delta 2.

Now notice which Cj you need. You need C63, which relies on C62, which relies on C60, which relies on C56, which relies on C48, which relies on C32, which relies on C0, G’s and P’s.

C0 is immediate. G’s and P’s takes delta of 11, which is 1+2*s, where s = log32(base 2).

In total, waiting for C32 takes 11, then we have a sequence of 32->48->56->60->62->63->FA->result

in total, addition of 7*2 = 14.

11+ 14 = 25.