Algebraic Manipulation (1.8)

Algebraic Manipulation

• Boolean algebra is a useful tool for simplifying digital circuits.
• Why do it? Simpler is cheaper and smaller.
• Example: Simplify F= x’yz + x’yz’ + xz.

        F = x’yz + x’yz’ + xz   = x’y(z+z’) + xz = x’y•1 + xz = x’y + xz

•  Example: Prove x’y’z’ + x’yz’ + xyz’ = x’z’ + yz’

• Equal term has been added: if any term (equal to an already existing term) is being added, total value of the expression is not changed

  Proof:    x’y’z’+ x’yz’+ xyz’= x’y’z’ + x’yz’ + x’yz’ + xyz’= x’z’(y’+y) + yz’(x’+x)= x’z’•1 + yz’•1= x’z’ + yz’

                 QED