ECE 153a/253 Homework 2 Problems: 1. Consider the following FSM States: a,b,c,d,e Transitions: 0,a->b,1 1,a->c,0 0,b->b,0 1,b->d,0 0,c->a,0 1,c->c,0 0,d->c,1 1,d->e,0 0,e->a,0 1,e->c,0 Is this a minimal machine? If not, show a smaller equivalent machine. 2. A common method to keep track of spinning shaft is a quadrature encoder. Such an encoder has 2 sensors looking at 4 quadrants of the wheel. Numbering the quadrants clockwise, the encodings are: 1:a=0b=0; 2:a=0b=1; 3:a=1b=1; 4:a=1b=0 for the two sensors a and b. Turning clockwise, quadrants appear in counting order, with 1 following 4. Imagine that you need to make a counter that keeps a running total of the number of turns of the wheel -- clockwise increments the counter while counter clockwise decrements it. The counter is an external device, you must only supply the two signals: u for up or increment and d for down or decrement. You will need to count exactly once for each rotation of the wheel, meaning if the machine
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