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Simplify the following Boolean functions. F(w, x, y, z) = !w!x!y!z + w!x!y!z + wx!y!z + !w!xy!z + wxy!z + w!xy!z F(w, x, y, z)= *Please do not include "F(w, x, y, z)= " in your solution. Add a single space between variables and operators. answer

Simplify the following Boolean functions. F(w, x, y, z) = !w!x!y!z + w!x!y!z + wx!y!z + !w!xy!z + wxy!z + w!xy!z F(w, x, y, z)= *Please do not include "F(w, x, y, z)= " in your solution. Add a single space between variables and operators. answer

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Simplify the following Boolean functions. F(w, x, y, z) = !w!x!y!z + w!x!y!z + wx!y!z + !w!xy!z + wxy!z + w!xy!z F(w, x, y, z) = *Please do not include "F(w, x, y, z) = " in your solution. Add a single space between variables and operators. answer
Transcribed Image Text:Simplify the following Boolean functions. F(w, x, y, z) = !w!x!y!z + w!x!y!z + wx!y!z + !w!xy!z + wxy!z + w!xy!z F(w, x, y, z) = *Please do not include "F(w, x, y, z) = " in your solution. Add a single space between variables and operators. answer
Expert Solution
Step 1

!w is w¯

!x is x¯

!y is y¯

!z is z¯

So Question is-

F(w,x,y,z)=wxyz¯ +wxyz¯ + wxyz¯ +wx¯yz¯ + wxyz¯ + wx¯yz¯

               = wxyz¯ + wxyz¯ + wxyz¯ + wxyz¯ + wx¯yz¯ + wx¯yz¯

              =(w¯ + w) xyz¯ + wxz¯(y¯ + y) + x¯yz¯(w¯ + w)

               As Per Complement law A + A¯ = 1

             = xyz¯ + wxz¯ + x¯yz¯

             = xyz¯ + x¯yz¯ + wxz¯

             = xz¯(y¯ + y) +wxz¯

            Now Apply Complement law

            = xz¯ + wxz¯

          = z¯(x¯ + wx)

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