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generator tach- ometer At Damp bgic 1) You have been asked by a science museum to build the lamp logic for a stationary bicycle exhibit at the local science exhibition. As a rider increases his pedaling speed, lamps will light on a bar graph display. No lamps will light for no motion. As speed increases, the lower lamp, L1 lights, then L1 and L2, then, L1, L2, and L3, until all lamps light at the highest speed. Once all the lamps illuminate, no further increase in speed will have any effect on the display. A small DC generator coupled to the bicycle tire outputs a voltage proportional to speed. It drives a tachometer board which limits the voltage at the high end of speed where all lamps light. No further increase in speed can increase the voltage beyond this level. The lamp logic needs to respond to the six codes out of the Analog to Digital converter (A to Din the picture above). For ABC=000, no motion, no lamps light. For the five codes (001 to 101) lamps L1, L1&L2, L1&L28L3, up to all lamps will light, as speed, voltage, and the A to D code (ABC) increases. We do not care about the response to input codes (110, 111) because these codes will never come out of the A to D due to the limiting in the tachometer block. Design the logic circuits to drive the five lamps. Use K-Map simplification to obtain your functions and then implement the functions using AND and OR gates. Complete 2) the final circuit by connecting the LEDS (lamps L1 through L5) to your deesign. (25 points) Find all the prime implicants for the following Boolean functions and determine which are essential, then simplify the Boolean functions: (10 points) a) F(A, B, C, D) = {(2,3,4,5,6,7,9,11,12,13) b) F(w,x,y,z) = (0,1,2,5,7,8,10,15) 3) Convert the following Boolean function from a sum of products to a simplified product of sums form (5 points) F(w,x,y,z) = 3 (0,1,2,5,8,10,13) 4) Simplify the following Boolean function F, together with the don't care conditions d, and then express the simplified function in sum of minterms form: (10 points) a) F(x,y,z) = {m (0,1,4,6) + d(2,3,7) b) F(A,B,C,D) = {m(4,12,7,2,10) +