9) A washing machine that uses liquid soap adds the soap into the tub on one of four conditions as described below. For any of these, a sensor must detect soap in the soap dispenser unit. The tub has completed filling with water at the beginning of the cycle The timer has reached one of two soap cycles The soap button is pressed The washing machine is set to extra soap instead of normal and the timer has reached halfway In order to determine when soap should be applied, there are a number of sensors/timers. First, there is the mode which is set to normal or extra soap. This is denoted by m= 1 (normal) or m=0 (extra soap). Next is a 3-bit timer to indicate what part of the cycle the washing machine is at. The timer is denoted as t2ti to which, at 001, means the tub has completed filling with water and the cycle is beginning, and 011 and 101 indicate the start of the two soap cycles. The halfway point is indicated by the value 100. The soap button is indicated by sensor si (1 for apply soap, 0 otherwise). Finally, sensor so indicates soap is in the dispenser with 1 meaning soap is available and 0 means no soap. a. Provide the Boolean expression that is 1 if soap should be applied and 0 otherwise. If you can reduce the expression, do so for extra credit but provide the original. b. Draw the circuit of the expression (whether original or reduced) from part a. 9) A washing machine that uses liquid soap adds the soap into the tub on one of four conditions as described below. For any of these, a sensor must detect soap in the soap dispenser unit. The tub has completed filling with water at the beginning of the cycle The timer has reached one of two soap cycles The soap button is pressed The washing machine is set to extra soap instead of normal and the timer has reached halfway In order to determine when soap should be applied, there are a number of sensors/timers. First, there is the mode which is set to normal or extra soap. This is denoted by m= 1 (normal) or m=0 (extra soap). Next is a 3-bit timer to indicate what part of the cycle the washing machine is at. The timer is denoted as t2ti to which, at 001, means the tub has completed filling with water and the cycle is beginning, and 011 and 101 indicate the start of the two soap cycles. The halfway point is indicated by the value 100. The soap button is indicated by sensor si (1 for apply soap, 0 otherwise). Finally, sensor so indicates soap is in the dispenser with 1 meaning soap is available and 0 means no soap. a. Provide the Boolean expression that is 1 if soap should be applied and 0 otherwise. If you can reduce the expression, do so for extra credit but provide the original. b. Draw the circuit of the expression (whether original or reduced) from part a
