Boolean-Functions
Question 1 |
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?
XOR gates, NOT gates | |
2 to 1 multiplexors | |
AND gates, XOR gates | |
Three-input gates that output (A⋅B) + C for the inputs A⋅B and C | |
Both B and C |
Question 1 Explanation:
(A) Not complete because, XOR can be used to make only NOT gate and NOT gate is already available. Hence not complete.
(B) 2 to 1 multiplexors is functionally complete.
(C) XOR gate can be used to make a NOT gate. So, (AND, NOT) is functionally complete.
(D) With given gates and inputs NOT gate cannot be derived.
Hence, not complete.
(B) 2 to 1 multiplexors is functionally complete.
(C) XOR gate can be used to make a NOT gate. So, (AND, NOT) is functionally complete.
(D) With given gates and inputs NOT gate cannot be derived.
Hence, not complete.
Question 2 |
The majority function is a Boolean function f(x, y, z) that takes the value 1 whenever a majority of the variables x, y, z and 1. In the circuit diagram for the majority function shown below, the logic gates for the boxes labeled P and Q are, respectively,
XOR, AND | |
XOR, XOR | |
OR, OR | |
OR, AND |
Question 2 Explanation:
Thus we have OR and AND which gives different outputs on (0,0) and (1,1).
The encodes can be hence select from the two and decide output of the function according to x.
There are 2 questions to complete.