distributive law A B A B AA AB BA BB distributive law A B A B 0 AB BA 0

Distributive law a b a b aa ab ba bb distributive law

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distributive law(A’ * B) + (A * B’) = A*A’ + A*B’ + B*A’ + B*B’ distributive law(A’ * B) + (A * B’) = 0 + A*B’ + B*A’ + 0 identity x*x’ = 0(A’ * B) + (A * B’) = A’*B + A*B’ simplify: QED.
3. (5) Complete the truth table below that defines the circuit outputs Y and X as afunction of the inputs A and B.4. Consider the following circuit: a) (5) If S=1 show the outputs if initially I3, I2 , I1 I0 = 1001.O3 = _____1_____O2 = _____1_____O1 = _____0_____O0 = _____0_____b) (5) If S=0 show the outputs if initially I3, I2 , I1 I0 = 1001.O3 = ____0_____O2 = ____0_____O1 = ____1_____O0 = ____0_____ABXY0000010110011110
5. (5) Use Boolean identities (not truth tables) to show that the following expressionis true: (A ^ B)’ = A’ * B’ + A * B DeMorgan’s theorem: (X+Y)’ = X’ * Y’DeMorgan’s theorem: (X*Y)’ = X’ + Y’(A ^ B)’ = (A’ * B + A * B’)’ definition of ^ (XOR)(A ^ B)’ = (A’ * B)’ * (A * B’)’ DeMorgan’s theorem(A ^ B)’ = (A’’ + B’) * (A’ + B’’)DeMorgan’s theorem(A ^ B)’ = (A + B’) * (A’ + B) identity x’’ = x(A ^ B)’ = A*A’ + A * B + B’ * A’ + B’ * B distributivity(A ^ B)’ = 0 + A * B + B’ * A’ + 0identity x*x’ = 0(A ^ B)’ = A’ * B’ + A * Bsimplify & associativity: QED 6. The 8-digit hex number 0x00000000 corresponds to a 32-bit MIPS machine instruction. a) (3) What ALU operation is performed by this instruction? b) (2) What are the ALU inputs? . c) (3) What is the value of the 32-bit result that is produced? d) (2) Which CPU general purpose registers are modified when the instruction executes?

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