2 October events (Boolean algebra) Consider the month of October, 2017. It has 31 days (1-31), each with 24 hours (0-23 la military time). We carn represent each by 5 bit numbers d 4d3d2dido, h = h4h3h2hiho respectively: we will create svstems taking these 10 bits as inputs. 2.3 Does this even make sense? 2.3(a). Not all sets of 10 input bits correspond to a valid date and/or time. Write the function-using minterm or maxterm shorthand-that returns true if the 10 bit input is valid, and false otherwise. 2.3(b). Find the simplest boolean expression for this function. Hint: this will not be a canonical normal form, and will contain only 7 literals along with a number of operators. 2.3(c). Write the dual of this expression. 2.4 Don't care. If we specify a set of valid inputs for our system, we can choose what value our function assigns to invalid inputs "don't care" values) whichever way we would like in order to simplify our boolean expressions 2.4(a). If we assume that our 5 bit input will represent a valid hour, come up with a simple boolean expression (using no more than 3 literals) that returns true if the hour is a valid afternoon hour and false if it is a valid morning hour. 2.4(b). If instead we specify that the function must also be false for invalid hours, does the boolean expression change? If so, what is the new expression? 2.4(c). Draw this function using only NOR gates 2 October events (Boolean algebra) Consider the month of October, 2017. It has 31 days (1-31), each with 24 hours (0-23 la military time). We carn represent each by 5 bit numbers d 4d3d2dido, h = h4h3h2hiho respectively: we will create svstems taking these 10 bits as inputs. 2.3 Does this even make sense? 2.3(a). Not all sets of 10 input bits correspond to a valid date and/or time. Write the function-using minterm or maxterm shorthand-that returns true if the 10 bit input is valid, and false otherwise. 2.3(b). Find the simplest boolean expression for this function. Hint: this will not be a canonical normal form, and will contain only 7 literals along with a number of operators. 2.3(c). Write the dual of this expression. 2.4 Don't care. If we specify a set of valid inputs for our system, we can choose what value our function assigns to invalid inputs "don't care" values) whichever way we would like in order to simplify our boolean expressions 2.4(a). If we assume that our 5 bit input will represent a valid hour, come up with a simple boolean expression (using no more than 3 literals) that returns true if the hour is a valid afternoon hour and false if it is a valid morning hour. 2.4(b). If instead we specify that the function must also be false for invalid hours, does the boolean expression change? If so, what is the new expression? 2.4(c). Draw this function using only NOR gates