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}

 

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