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ECE620_hw1sol

# ECE620_hw1sol - ECE 620 Dr R ROOSTA H.W 1 SOLUTIONS P1 For...

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ECE 620 Dr. R. ROOSTA H.W # 1 SOLUTIONS P1.) For the given circuit, the logic equations are : S1 = x'y2 + xy1'y2' S2 = x' + y1'y2' R1 = y1y2' R2 = xy2 z = x'y2 + xy1'y2' + y1y2 Plotting these expressions on a Karnaugh Map yields the excitation matrix as shown below : EXCITATION MATRIX The Y, z-matrix is derived from the excitation matrix. For example, the entry in row 11 and column 1 has S1 = R1 = 0 and therefore the variable y does not change state (i.e. y1 = 1) . Y-z MATRIX

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Associating the labels, A,B,C,D with codes 00, 01, 11, 10, respectively, we obtain the following state table: P2.) At time t1, the machine is assumed to be in the initial state A. While in this state, the machine can receive either an input 0 or 1. The arc labeled 1/0 forms a self-loop around state A, since the machine does not initiate the detection process until it receives a 0 input. An input 0 indicates a possible start of the sequence to be detected. Following the same idea, the state diagram is built as shown below. A 0 input applied to the machine
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ECE620_hw1sol - ECE 620 Dr R ROOSTA H.W 1 SOLUTIONS P1 For...

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