EEM16 – Fall 2008 - DISCUSSION #2 Problem 1: Conversion of bases a) Find y, u, v, and w in the following equations: 28B (base 12) = y (base 14) 5A1 (base 11) = u (base 7) 245 (base 7) +312 (base 6) = v (base 9) w (base 4) such that it is larger than 40 (base 5), smaller than 40 (base 11), and has the largest sum of digits in base 10 Problem 2: Switching functions a) Using boolean algebra, prove the following: x’y’z’ + x’y’z + x’yz + xy’z + xyz = x’y’ + z ABC’ + A’C’D + AB’C’ + BC’D + A’D= AC’ + A’D b) Express each of the three functions in part (a) in sum of minterms ( Σ m) and product of maxterms ( Π M) forms. c) Prove or disprove the following: f XOR (f AND (x1, x0), f AND (x1, x0)) = f EQUIVALENCE (x1, x0) f NAND (f NAND (x1, x0), f NAND (x1, x0)) = f AND (x1, x0) d) A symmetric switching function is one whose value does not change when its arguments are permuted. For example, the OR function is symmetric as f (a, b) = a OR b = b OR a = f(b, a). Of all possible switching functions
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