Q: Assistance in understanding and solving this example on Digital Design and Co
ID: 3743554 • Letter: Q
Question
Q: Assistance in understanding and solving this example on Digital Design and Computer Architecture college book with the steps of the solution to better understand, thanks.
a) Fill the blanks below with axiom & theorem names A1 to A5, A1' to A5' (for duals), T1 to T12, and T1' to T12' (for duals).
The equation X + (XY) + 1 is equal to X + 1 because of theorem ______________, and X + 1 itself is equal to 1 because of theorem ________ .
The equation X(X+Z) + X is equal to X + X because of theorem __________, and X + X itself is equal to X because of theorem ____________.
b) Which of the four instructions given as choices, correctly matches the description: "this instruction will double the numeric value stored in $t1"?
addi $t1, 2, 2
add $t1, $t1, 2Explanation / Answer
A1..A5 theorem is not provided in question
by Idempotent law
X + X = X
by Annulment Law
X + 1 = 1
equation X + (XY) + 1 is equal to X + 1 because of theorem _________,
and X + 1 itself is equal to 1 because of theorem Annulment .
The equation X(X+Z) + X is equal to X + X because of theorem __________,
and X + X itself is equal to X because of theorem __Idempotent ___.
b)
add $t1, $t1, $t1
both t1's will be added
t1 + t1 = 2t1
and place it in t1
So t1 will become twice of itself.
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