Logic Circuit Design

# Logic Circuit Design - B B A D C B A f C B A BD AB D C B A...

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Assignment 1 (EE2000) Q1. Use 2’s complement representation of the subtrahend to perform the following subtraction and verify your results in decimal number system. Noted that the numbers are in un-signed representation. (a) 10110 - 1101 (b) 10111 - 110100 Q2. Use Boolean algebraic theorems to prove the following Boolean identities: (a) ( x+y ) ( y+z ) ( x+z ) = xy +yz + xz (b) ) ( ) ( ) ( z y x z x y x = + + Q3. Write down the SOP form of the circuit shown in Figure Q3. With the aid of DeMorgan’s Theorem, turn the SOP Boolean expression into a form that can be implemented using (i) NAND gates, and (ii) NOR gates, only. Draw the circuit diagrams. f x y v w z y w u Figure Q3 Q4. Given the as follows, using K-map to find βα f f and f f f = 1 , , f f f = 2 and . f f f = 3 D
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Unformatted text preview: B B A D C B A f C B A BD AB D C B A f + = + + = ) , , , ( ) , , , ( β α Q5. Find the minimum POS expression of the following Boolean function. F (a, b, c, d)= Σ m(1, 4, 5, 6, 7, 9, 11, 13) + Σ dc(3, 10, 14, 15) Q6. A Boolean function expression in maxterm representation is given by F(A, B, C, D) = Π M (0, 2, 3, 7, 8, 9, 10, 13) Use K-map to find the product of sum (POS) representation of F(A, B, C, D) if minimum maxterm is required. Q7. Using the Quine-McCluskey method to simplify the Boolean expression and the result should be POS form. (hint: you may carry the grouping according to the number of 0, instead of 1.) f ( w,x,y,z ) = ∏ M (3,4,5,8,9,11,13,14,15)...
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