1) Write the following as a Boolean expression
a) The company safe should be unlock only when Mr. Jones is in the office or Mr. Evans is in the office, and only when the company is open for business, and only when the security guard is present.
b) The elevator door should open if the elevator is stopped, it is level with the floor, and the timer has not expired, or if the elevator is stopped, it is level with the floor, and a button is pressed.
2) A flow rate sensing device used on a liquid transport pipeline functions as follows. The device provides 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 if the flow rate is at least 10 gallons per minute; the first and second bits are 1 if the flow rate is at least 20 gallons per minute; the first, second, and third bits are 1 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 and E are used as inputs to a device that provides two outputs Y and Z.
a) Write an equation for the output Y if we want Y to be 1 iff the flow rate is less than 30 gallons per minute.
b) Write an equation for the output Z if we want Z to be 1 iff the flow rate is at least 20 gallons per minute but less than 50 gallons per minute.
3) A circuit has four inputs as shown. A and B represent the first and second bits of a binary number N1. C and D represent the first and second bits of a binary number N2. The output is to be 1 only if the product of N1 * N2 is less than or equal to 2.
a) Find the minterm expansion for F
b) Find the maxterm expansion for F
4) Given F(a,b,c) = abc' + b'
a) Express as a minterm expansion
b) Express as a maxterm expansion
5) Four chairs (A, B, C, and D) are placed in a circle: A next to B, B next to C, C next to D, and D next to A. Each chair may be occupied (1) or empty (0). Give the minterm and maxterm expansion for:
a) F(A,B,C,D) is 1 iff there are no adjacent empty chairs.
b) G(A,B,C,D) is 1 iff there are at least three adjacent empty chairs.
c) H(A,B,C,D) is 1 iff at least three chairs are full.