K Maps · Digital Logic · GATE CSE

Consider the following interm expression of $$F:$$
$$F\left( {P,\,Q,\,R,\,S} \right) = \sum {0,2,5,7,8,10,13,15} $$
The minterms $$2, 7, 8$$ and $$13$$ are 'do not care' terms. The minimal sum-of-products form for $$F$$ is _______

In the Karnaugh map shown below, $$X$$ denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

Minimum $$SOP$$ for $$f(w, x, y, z)$$ shown in karnaugh $$-$$ map below is

Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?

Which of the following functions implements the Karnaugh map shown below?

Consider the following 4-variable Boolean function

$$ F(A, B, C, D)=\Sigma m(0,1,2,3,8,9,10,11) $$

Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents the minimal sum of products form for the above function?

Note: + is OR operation, • is AND operation, ' is NOT operation

Consider a Boolean function $F$ with the following minterm expression:

$$ F(P, Q, R, S)=\Sigma m(1,2,3,4,5,7,10,12,13,14) $$

Which of the following options is/are the minimal sum-of-products expression(s) of $F$ ?

Given the Following Karnaugh Map for a Boolean function $F(w,x,y,z)$:

Which one or more of the following Boolean expression(s) represent(s) F?

Consider the following four variable Boolean function in sum-of-product form

$$F\left(b_3, b_2, b_1, b_0\right)=\Sigma(0,2,4,8,10,11,12)$$

where the value of the function is computed by considering $b_3 b_2 b_1 b_0$ as a 4-bit binary number, where $b_3$ denotes the most significant bit and $b_0$ denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for $F$ ?

What is the minimum number of 2-input NOR gates required to implement a 4-variable function function expressed in sum-of-minterms form as

f = Σ(0, 2, 5, 7, 8, 10, 13, 15)?

Assume that all the inputs and their complements are available.

Consider the minterm list form of a Boolean function 𝐹 given below. $$F\left( {P,Q,R,S} \right) = $$ $$\sum {m\left( {0,2,5,7,9,11} \right)} $$ $$ + \,\,d\left( {3,8,10,12,14} \right)$$

Here, $$m$$ denotes a minterm and $$d$$ denotes a don’t care term. The number of essential prime implicants of the function $$F$$ is ___________.

What is the minimal form of the Karnaugh map shown below? Assume that $$X$$ denotes a don’t care term.

Consider a multiplexer with $$X$$ and $$Y$$ as data inputs and $$Z$$ as control input. If $$z=0$$ select input $$x,$$ and $$z=1$$ selects input $$Y$$. what are the connections required to realize the $$2-$$variable Boolean function $$f=T+R$$ without using any additional Hardware?

The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of $$(xy + xz)$$ is $$4.$$ What are the minimum possible literal counts of the product -of -sum and sum -of-product representations respectively of the function given by the following Karnaugh map? Here, $$X$$ denotes “don’t care”

Which function does NOT implement the Karnaugh map given below?

What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in fig?