Q: Assistance in understanding and solving this example on Digital Design and Co

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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.

Boolean Theorems of several variables (A1 thru A5, A1',A4',A5', T1 thru T12, T1' thru T12' ).

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 write the value inside memory location addressed by 24 (that's the decimal number 24) into the register $t2"?.

Explanation / Answer

X+XY+1=X(1+Y)+1 and Y+1=1 by Dominance law

X+1 again by Dominance law X+1=1

2) X(X+Z)+X (considering z=0)

XX+XZ+X

Now XZ=0 by Dominance law and XX=X by Idempotence law

X+X again using Idempotence law X+X=X

B) sw $t2, 0x24($0) because sw is to write onto memory location $t2 from memory locations $0+24 and $0 contain 0.

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