1.

Give the Boolean function F(w,x,y,z)=(1,2,3,5,7,9,11,13,15) reduce it by k-map in sop form

Answer»

Answer:

w'x'y + Z

Explanation:

We have:

\begin{array}{c c c}\rm Decimal & \rm Binary & \rm Corresponding \ Angle \\1 & 0001 & \rm w'x'y'z' \\2 & 0010 & \rm w'x'<klux>YZ</klux>' \\3 & 0011 & \rm w'x'yz \\5 & 0101 & \rm w'xy'z \\7 & 0111 & \rm w'xyz \\9 & 1001 & \rm wx'y'z \\11 & 1011 & \rm wx'yz \\13 & 1101 & \rm <klux>WXY</klux>'z \\15 & 1111 & \rm wxyz\end{array}

Since we're using SOP form,

add EM'

w'x'y'z + w'x'yz' + w'x'yz + w'xy'z + w'xyz + wx'y'z + wx'yz + wxy'z + wxyz

Reduce it,

w'x' (y'z + yz' + yz) + w'x (y'z + yz) + wx'( y'z + yz) + wx (y'z + yz)

=w'x' ( y'z + y) + w'x (z) + wx' (z) + wx (z)

= w'x' ( y'z + y)  + w'xz + wx'z + wxz

=w'x' ( y+z )  + w'xz + WZ        [A'B + B =A+B]

=w'x'y +w'x'z + w'xz + wz

=w'x'y + w'z + wz

=w'x'y + z


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