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hw2_sol - ECE341 Homework No 2 Solution Problem No 1 The...

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ECE341 Homework No. 2 Solution Problem No. 1 The modified shift register is as follows: Problem No. 2 (a) gG±1, ±2, ±3, ±4² ³ ±1. ±2 ´´´ . ±3 µ ±2. ±3. ±4 µ ±2 . ±3 We choose x1, x2 and x3 as selector inputs. The resulting 8-input multiplexer circuit is as follows:
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(b) We choose x2 and x3 as selector inputs. This is a logical choice since x2 and x3 appear in all the product terms for function f . The resulting 4-input multiplexer circuit is as follows:
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Problem No. 3 State variables y 1 and y 2 are used to express each state as a 2-bit number y 2 y 1 . According to the problem statement, the following state assignment is used: S0 = 01, S1 = 10, S2=11, and S3=00. We use the state table for the mod-4 up/down counter discussed in class and replace each state with its state assignment. The resultant stat-assigned state table is as follows: Present State Next State Output z x = 0 x = 1 y 2 y 1 Y 2 Y 1 Y 2 Y 1 01 10 00 0 10 11 01 0 11 00 10 1 00 01 11 0 Logic expressions to implement this state machine are as follows: g2 G ±2 ²²² . ±1. ³̅ ´ ±2. ±1
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