Problem-50

Problem-50

Find the sum-of-products expansions of these Boolean functions.

a) F(x,y,z)=x+y+z

b) F(x,y,z)=(y+x)z

c) F(x,y,z)=y

d) F(x,y,z)=x $\overline{y}$

Solution

a) F(x,y,z)=x+y+z

$xyz+xy\overline{z}+x\overline{y}z+x\overline{y}\overline{z}+\overline{x}yz+\overline{x}y\overline{z}+\overline{x}\overline{y}z$

b) F(x,y,z)=(y+x)z

$xyz=x\overline{y}z+\overline{x}yz$

c) F(x,y,z)=y

$xyz+\overline{x}yz+xy\overline{z}+\overline{x}y\overline{z}$

d) F(x,y,z)=x $\overline{y}$

$x\overline{y}z+x\overline{y}\overline{z}$