Post date: Feb 10, 2011 4:14:00 PM
Content:
Use algebraic manipulation to prove a boolean equation.
Sum of Product Form
Product of Sum Form
Minterm expansions
Assignment 8:
Textbook, p91 2-2
(c) y+x'z+xy'=x+y+z
(d) x'y'+y'z+xz+xy+yz'=x'y'+xz+yz'
Answers:
(c)
=y+xy'+x'z
=(y+x)(y+y')+x'z
=y+x+x'z
=y+(x+x')(x+z)
=y+x+z
(d)
=x'y'+(x+x')y'z+xz+xy(z+z')+yz'
=x'y'+xy'z+x'y'z+xz+xyz+xyz'+yz'
=(x'y'+x'y'z)+(xy'z+xz)+xyz+(xyz'+yz')
=x'y'(1+z)+xz(y'+1)+xyz+(x+1)yz'
=x'y'+xz+xyz+yz'
=x'y'+xz(1+y)+yz'
=x'y'+xz+yz'
Minterm Expansion
xy+y'z'+x'z'
Answer:
=xy(z+z')+(x+x')y'z'+x'(y+y')z'
=xyz+xyz'+xy'z'+x'y'z'+x'yz'+x'y'z'
=m7+m6+m4+m0+m2
Click here for solutions for chapter 2, check it as samples and practice makes perfect!