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4. A flow rate sensing device used on a liquid transport pipeline functions as follows. The device produces a 5-bit output where all five bits are zero if the flow rate is less than 10 gallons per minute. The first bit is 1 (and all others zero) if the flow rate is at least 10 gallons per minute; the first and second bits are 1 (and all others zero) if the flow rate is at least 20 gallons per minute; the first, second, and third bits are 1 (and all others zero) if the flow rate is at least 30 gallons per minute; and so on. The five bits, represented by the logical variables (A, B,C, D, E) are used as inputs to a device that provides two outputs Y and Z. Use the truth table below for this problem. Show all your work without omitting any details 4a. Write a minimum SOP equation for the output Y if we want Y to be 1 if and only if the flow rate is less than 30 gallons per minute. (10 points). 4b. Write a minimum SOP equation for the output Z if we want Z to be 1 if and only if the flow rate is at least 20 gallons per minute but less than 50 gallons per minute. (10 points). Decimal IABICID 0 0 1 00 0 01 01 0 10 0 0 10 01 0 1 0 0 11 0 1 1 1 1 14 15 16 17 18 19 20 21 23 24 25 26 27 28 29 30 31 111 00