Question

if a Boolean function is represented by join of minterms then it is said to be​

Answer 1

Answer:

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A Boolean function is described by an algebraic expression consisting of binary variables, the constants 0 and 1, and the logic operation symbols +,\:.\:,\:^\prime

Any binary variable can take one of two forms, x or x^\prime. A boolean function can be expressed in terms of n binary variables. If all the binary variables are combined together using the AND operation, then there are a total of 2^n combinations since each variable can take two forms.

Each of the combinations is called a minterm or standard product. A minterm is represented by m_i where i is the decimal equivalent of the binary number the minterm is designated.

In a similar way, if the variables are combined together with OR operation, then the term obtained is called a maxterm or standard sum. A maxterm is represented by M_i where i is the decimal equivalent of the binary number the maxterm is designated.

Step-by-step explanation:

For a given set of values of the binary variables involved, the boolean function can have a value of 0 or 1. For example, the boolean function F= x^\prime y + z is defined in terms of three binary variables x,\:y,\:z. The function is equal to 1 if x=0 and y=1 simultaneously or z=1.

Every boolean function can be expressed by an algebraic expression, such as one mentioned above, or in terms of a Truth Table. A function may be expressed through several algebraic expressions, on account of them being logically equivalent, but there is only one unique truth table for every function.

A Boolean function can be transformed from an algebraic expression into a circuit diagram composed of logic gates connected in a particular structure. Circuit diagram for F–

In a minterm, the binary variable is un-primed if the variable is 1 and it is primed if the variable is 0 i.e. if the minterm is xy^\prime then that means x=1 and y=0.

For example, for a boolean function in two variables the minterms are –

m_0=x^\prime y^\prime,\:m_1=x^\prime y,\:m_2=x y^\prime,\:m_3=x y

In a maxterm, the binary variable is un-primed if the variable is 0 and it is primed if the variable is 1 i.e. if the maxterm is x^\prime+y then that means x^\prime=1 and y=0.

For example, for a boolean function in two variables the maxterms are –

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