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sol1_06 - 06-1 Boolean Expressions and K-map(20 Given a...

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2006 Elec151 Solution of Midterm Exam #1, p1/7 06-1. Boolean Expressions and K-map (20%) Given a Boolean function F(A,B,C,D) = Σ m(1,2,3,11,12,14) + d(0, 7, 15) a). Simplify this Boolean function in sum of minterms. (5%) b). Simplify this Boolean function in product of maxterms. (10%) c). In CMOS technology, what is the minimum number of transistors required to implement this function in two-level design. (5%) a). Re-express F in K-map F = A’B’ + CD + ABD’ b) Re-express F’ in K-map F’ = A’B + AB’D’ + AC’D F = (A+B’) (A’+B+D) (A’+C+D’) c) The sum-of-minterms requires fewer gates or transistors. After being transferred to 2-level NAND gates, it consists of 3 inverters (for A, B and D), 2 2-input NAND gates and 2 3-input NAND gates for a total of 0.5 x 3 + 1 x 2 + 1.5 x 2 = 6.5 equivalent gates , or 6.5 x 4 = 26 transistors AB 00 01 11 10 X 1 0 1 0 1 1 1 0 X X 0 0 1 0 1 00 01 11 10 CD AB 00 01 11 10 X 0 1 0 1 0 0 0 1 X X 1 1 0 1 0 00 01 11 10 CD 2006 Elec151 Solution of Midterm Exam #1, p2/7 06-2. Multilevel Logic and Analysis (20%)) Obtain the most simplified Boolean expressions for output F and G in 2-level sum of minterms. (20%) F = (A+D)(A’+BC) = A’D + ABC + BCD
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