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Switching Circuits and Logic Design Quiz 1 14:20 ~ 15:10, October 16, 2008 1. Add the following numbers in binary using 2’s complement to represent negative numbers. Use a word length of 6 bits (including sign) and indicate if an overflow occurs. a) [10 points] ( 23) 11 - + b) [10 points] ( 18) ( 17) - + - 2. [15 points] Factor the following expression to obtain a minimum product-of-sums. ' ' F AB CD E = + + 3. [15 points] Prove ( ) ( ) x y z x y z ⊕ = ⊕ and [15 points] find its minimum sum-of-products expression. 4. A full adder has three inputs ( , , ) in X Y C
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Unformatted text preview: and two outputs ( , ) out Sum C . a) [10 points] Please write the Boolean expression of out C in minimum sum-of-products. b) [15 points] Please write the minterm expansion of (?) Sum m = ∑ . Suppose that X is the most significant bit and C in is the least significant bit. That means: ( , , ) (1,0,0) in X Y C = represents 4 m . ( , , ) (0,0,1) in X Y C = represents 1 m . 5. [10 points] Suppose that ( , , , ) (0,2,3,4,5,10,11,12,13,15) F A B C D M = ∏ . Please show ' F in minterm expansion....
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