Combinatorics | Number Theory Answers

For the function: F(W,X,Y,Z) = "\\prod" M(0,3,4,6,7,9,11,15):

a) identify the essential prime implicants

b) Write the minimal sum

For the functions below:

i) G (W,X,Y,Z) = Σm (1, 4, 7, 8, 9, 11) + d (0, 3, 5)

ii) F (A, B, C, D) = Σm (7, 9, 12, 13, 14, 15) + d (4, 11)

iii) F (A, B, C, D) = πM (2, 8, 11, 15) + d (3, 12, 14)

iv) F (W, X, Y, Z) = πM (0, 2, 6, 11, 13, 15) + d (1, 9, 10, 14)

a) Identify the essential prime implicants

b) Write the minimal sum/product

c) Implement with NAND gates only

d) Implement with NOR gates only

Draw the multiple-level NOR circuit for the following expression: CD(B + C)A + (B"\\bar{ C}" + D"\\bar E" )

Draw a logic diagram using only two-input NOR gates to implement the following

function: F(A, B, C, D) = "\\overline {(A\\bigoplus B)}(C\\bigoplus D)"

A large building has a hallway with two doors at opposite ends. There is a light bulb in the hallway that is controlled by three switches: the first switch (S1) is attached to the first door, the second switch (S2) is attached to the second door and the last switch (S3) is in the hallway. The two switches (S1 and S2) are closed when their respective doors open and open when their respective doors close. The third switch (S3) is closed when there is movement in the hallway. Otherwise, it remains open. The light bulb in the hallway is switched on when either S1 or S2 is closed, or if there is movement in the

hallway. If both doors are open at the same time, the light bulb is switched off.

a) Model the circuit and draw a truth table to show its behavior.

b) Minimize the function for the circuit and implement using only NAND gates