CSE140 Midterm1_Solution

# CSE140 Midterm1_Solution - CSE140 Midterm 1 Name...

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1 CSE140 Midterm 1, October 14, 2010, Name___________________________ PID ----------------------------- (I) (15pts) (Problem Formulation and Canonical Expression) A full adder inputs three bits ( a , b , cin ) and outputs the sum bit and carry bit ( s , cout ). Write the truth table of the full adder and the corresponding canonical product-of- maxterms expressions. A B Cin S Cout 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 S = (a + b + cin)(a + b' + cin')(a' + b + cin')(a' + b' + cin) Cout = (a + b + c)(a' + b + cin)(a + b' + cin)(a + b + cin')

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2 (II) (10pts) (Laws and Theorems of Boolean Algebra) Specify the axioms or theorems for each step. Prove using Boolean algebra that a b + a’c’ + b’c’ = a’b + b’c’ . a’b + a’c’ +b’c’ = a’b + a’c’(b+b’) + b’c’ (complementarity) = a’b + a’c’b + a’c’b’ + b’c’ (distributivity) = a’b + b’c’ (Absorptio n of the first two and last two terms) Can also use Consensus directly to prove the result.
3 (III) (10pts) (Laws and Theorems of Boolean Algebra) Specify the axioms or theorems for each step. Prove using Boolean algebra that ( a’ + b )( a’ + c’ )( b +

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