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
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)
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.