Write the simplified equation for the given K-Map.

A. \(Y = \overline {{B_1}} {B_2} + \overline {{B_2}} {B_1}\)

B. \(Y = \overline {{B_3}} {B_0} + \overline {{B_4}} {B_3}\)

C. \(Y = \overline {{B_3}} {B_2} + \overline {{B_2}} {B_3}\)

D. \(Y = \overline {{B_1}} {B_0} + \overline {{B_0}} {B_1}\)

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Concept:

K-map:

K-map (Karnaugh Map) is a pictorial method used to minimize Boolean expression without having to use Boolean Algebra theorems and equation manipulation.
K-map can be thought of as a special version of a truth table.
Using K-map, expression with two to four variables are easily minimized.
K-maps are also referred to as 2D truth tables as each K-map is nothing but a different format of representing the values present in a one-dimensional truth table.
To simplify a logic expression with two inputs, we require a K-map with 4 cells (= 2²)
Similarly, a logic expression with four inputs we require a K-map with 16 cells (= 2⁴)
Each cell within K-map has a definite place value which is obtained by using on encoding technique known as Gray code.
For n-variable K-map, with 2ⁿ cells, try to group 2ⁿ cells first, then for 2^n-1 cells, next for 2^n-2 cells, and so on until the group contains only 2° cells ie. Isolated bits (if any)
Also remember, the number of cells in a group must be equal to an integer power to 2 i.e. 1, 2, 4, 8, ….

Calculation:

→ There are no 16 bits group, no 8-bits group, but there are 2-four bits group

→ Eliminate the variables for which the corresponding hit appears within the group as both 0 and 1.

→ Therefore in SOP form (sum of products) output Y = B̅₁ B₂ + B̅₂ B₁