hmwk2

# hmwk2 - x =(0 1 1 1 1 0 will not have output 6 as...

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CSM51A Homework 2 UCLA TAs: Pouya Dormiani, Gabriel Pan Assigned: Friday 10/05/07 Due: Friday 10/12/07 Problem1 Simplify a + a b + a b c + a b c d + a b c d Problem2 The XOR operator is denoted by the symbol and defined by the identity x 1 x 0 = x 1 x 0 + x 1 x 0 . Show that XOR operator is, 1. Commutative 2. Associative 3. Distributive with respect to and ( hint: x ( z y ) = ( xz ) ( xy )). Problem 3 Prove / Disprove the following: 1. if x y = 0 then x = y 2. x y = ( x y ) 3. x y = x y 4. if x y = z y then x = z 5. x x x x x . . . x is 0 for an even number of x ’s and x for an odd number of x ’s. Problem 4 Do Exercise 2.54 in the book with the following twist. The output z is not the position of the leading digit, but rather, the number of leading zeros in the input plus one. For example the input

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Unformatted text preview: x = (0 , 1 , , 1 , 1 , 1 , , 0) will not have output 6 as speciﬁed by the problem but rather, the output z will be two. Another example, given the input x = (0 , , , , 1 , , , 0), the output is z = 5. Don’t worry about part c (you don’t need to give the gray code representation of the output). Problem 5 Show the switching functions for the following expressions, 1. E ( x, y, z ) = xyz + x y + xyz 1 Problem 6 Convert the following switching expression into a sum of minterms, and express the result in m-notation via E ( w, x, y, z ). { [ w + ( xy + xyz + ( x + z )) ]( z + w ) } 2...
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