# Recent questions tagged functional-completeness

1
In GATE, I have seen a lot of questions where we are asked to check whether a set of operations is functionally complete or not. I know Functionally Complete and Partially Functionally Complete are two different things, but while marking answers in GATE, will we say a set is functionally complete even when it is partially functionally complete?
2
Is Ex-NOR functionally complete? pls explain in details
3
Show that $\{1,A \bar{B}\}$ is functionality complete, i.e., any Boolean function with variables $A$ and $B$ can be expressed using these two primitives.
1 vote
4
F(x, y, z) =x + y'z' It's functionally complete according to normal procedure to implement NOT & OR or AND from it. But from this short trick. https://www.google.co.in/amp/s/www.geeksforgeeks.org/gate-gate-cs-2015-set-1-question-49/amp It's preserving 1.so it can't be functionally complete. I must be wrong but I could not identify it.
5
Suppose a function F(A,B) = A' + B then to prove it functionally complete.Can we do it like:- F(A,A') = A' ----> Complementation derived F(A',B) = A + B -----> OR Operation Derived So we could conclude that its functionally Complete. Is it the right way if not Please tell the right eay to prove the Function to be Functionally Complete. Thank You in advance
1 vote
6
Which of the following set of components is sufficient to implement any arbitrary Boolean function? $XOR$ gates, $NOT$ gates $AND$ gates, $XOR$ gates and $1$ $2$ to $1$ multiplexer Three input gates that output $(A.B)+C$ for the inputs $A, B, C$
7
Which of the following set is not functionally complete? a) {XOR,1,NOT} b) {XOR,1,OR} c) {OR, NOT} d) {XOR,1, AND}
8
Consider the operations defined as f(X, Y, Z) = X'YZ + XY' + Y'Z' and g(X′, Y, Z) = X′YZ + X′YZ′ + XY . Iam following this method, A function is said to be complete if it can implement Complementation and OR logic / Complementation and AND logic. For function f(X,Y ... ans is X as X is complement of X', hence this is functionally incomplete). How to prove OR / AND logic is possible for f(X,Y,Z)?
9
Provide short answers to the following questions: Show that {NOR} is a functionally complete set of Boolean operations.
10
my doubt- I got first one not functionally complete but its partially complete because its use 0 for make a NOT gate please check
11
Any set of Boolean operators that is sufficient to represent all Boolean expressions is said to be complete. Which of the following is not complete ? {$NOT$, $OR$} {$NOR$} {$AND$, $OR$} {$AND$, $NOT$}
12
The implication gate, shown below has two inputs ($x \text{ and }y)$; the output is 1 except when $x =1 \text{ and } y=0\text{, realize }f=\bar{x}y+x\bar{y}$ using only four implication gates. Show that the implication gate is functionally complete.
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function? XOR gates, NOT gates $2$ to $1$ multiplexers AND gates, XOR gates Three-input gates that output $(A.B) + C$ for the inputs $A, B$ and $C$.