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sederhanakan fungsi boolean $F = wx + xy + yz + zw + w'x'yz' + w'x'y'z$ dengan melengkapi setiap variabel menggunakan sop lalu menggunakan peta karnaugh

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Product property of logarithms

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Q. sederhanakan fungsi boolean

F = wx + xy + yz + zw + w'x'yz' + w'x'y'z

dengan melengkapi setiap variabel menggunakan sop lalu menggunakan peta karnaugh

Identify Function and Method: Identify the given Boolean function and the method to simplify it. $\newline$ The given Boolean function is $F = wx + xy + yz + zw + w'x'yz' + w'x'y'z$ . We are asked to simplify it using the Sum of Products (SOP) form and then using a Karnaugh map.
Express in SOP Form: Express the function in SOP form. $\newline$ The function is already given in SOP form, where each term is a product (AND) of literals and the terms are summed (OR) together.
Create Karnaugh Map: Create a Karnaugh map for the given function. $\newline$ A Karnaugh map is a visual representation of a Boolean function that helps to simplify the function by grouping ones. Since we have four variables $w, x, y, z$ , we will create a $4$ -variable Karnaugh map with $16$ cells.
Fill Karnaugh Map: Fill in the Karnaugh map with the given function. $\newline$ We will place a $1$ in the cells corresponding to the minterms of the function and a $0$ in the other cells. The minterms are derived from the SOP form: $\newline$ - $wx$ corresponds to cells where $w=1$ and $x=1$ . $\newline$ - $xy$ corresponds to cells where $x=1$ and $y=1$ . $\newline$ - $yz$ corresponds to cells where $y=1$ and $0$ $0$ . $\newline$ - $0$ $1$ corresponds to cells where $0$ $0$ and $w=1$ . $\newline$ - $0$ $4$ corresponds to cells where $0$ $5$ , $0$ $6$ , $y=1$ , and $0$ $8$ . $\newline$ - $0$ $9$ corresponds to cells where $0$ $5$ , $0$ $6$ , $wx$ $2$ , and $0$ $0$ .
Group Ones for Simplification: Group the ones in the Karnaugh map to simplify the function. We look for groups of $1$ s that can be grouped in powers of two ( $1$ , $2$ , $4$ , $8$ , etc.). These groups should be as large as possible to simplify the function to the greatest extent. We also consider that the Karnaugh map ＂wraps around＂ so that cells on the edges can be grouped with cells on the opposite edge.
Write Simplified Function: Write down the simplified function from the groups in the Karnaugh map. Each group of $1$ s corresponds to a product term in the simplified function, where a variable is included if it is the same within the group and excluded if it varies. We combine all such product terms with $\text{OR}$ to get the simplified function.
Verify Simplified Function: Verify the simplified function. $\newline$ We need to ensure that the simplified function is indeed equivalent to the original function. This can be done by comparing the truth tables of the original and simplified functions or by logical reasoning.

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