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hmk1 - 9 The output z is deﬁned as 1 z = ± x 2 if x> 4...

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CSM51A Homework 1 UCLA TAs: Pouya Dormiani, Gabriel Pan Assigned: Monday 10/01/07 Due: Friday 10/05/07 Problem 1 A useful switching function is the majority switching function, defined by the following expression over the set { 0 , 1 } , Maj ( x, y, z ) = 1 , if two or three arguments are 1 0 , otherwise Show by comparison of tabular descriptions that, Maj ( a, b, Maj ( c, d, e )) = Maj [ Maj ( a, b, c ) , d, Maj ( a, b, e )] Hint: A simpler approach would be to consider separately the cases a = b = 0 , a = b = 1 , and a = b Problem 2 The table shown defines two three-valued functions. Determine the table for the function f ( a, b ) = f 2 ( b, f 1 ( a, b )). ab f 1 ( a, b ) f 2 ( a, b ) 00 1 1 01 2 0 02 0 1 10 1 0 11 0 2 12 2 0 20 0 0 21 1 1 22 2 0 Problem 3 Consider a function that takes as input two 2-bit positive numbers and produces as output a 3-bit sum. Write the table for these three switching functions. Problem 4 Consider the combinational system with one input x which represents a decimal digit, i.e.

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Unformatted text preview: 9 } . The output z is deﬁned as, 1 z = ± x 2 , if x > 4 2 x , otherwise (1) The input x is encoded via a 2421 code as described in Table 2.3 in the book. The output z consists of two digits encoded via 2421 code. Fill in the following table and then give a one-set and dc-set representation of each switching function f i . Z 1 3 Z 1 2 Z 1 1 Z 1 Z 3 Z 2 Z 1 Z x X 3 X 2 X 1 X f 7 f 6 f 5 f 4 f 3 f 2 f 1 f 1 2 3 4 5 6 7 8 9 Problem 5 Given a value x with representation X = X 3 X 2 X 1 X and weight vector W = ( W 3 ,W 2 ,W 1 ,W ) we recall that, x = 3 X i =0 X i W i Show that if the weight vector satisﬁes the following properties, X i W i = n then the complement of X, denoted as X = X 3 X 2 X 1 X satisﬁes, X = n-X . Hint: given a bit α , α = 1-α . 2...
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hmk1 - 9 The output z is deﬁned as 1 z = ± x 2 if x> 4...

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