Transforming a Non-Canonical Expression into a Canonical Expression

v Sum of Product

1) Identify missing variable in each AND term.

2) AND the missing term and its complement with the original AND term.

XY à XY * (Z + Z’) = XYZ + XYZ’

Notes: (Z + Z’) = 1

3) Expand the terms by applying the property of distribution.

v Product of Sum

1) Identify missing variable in each OR term.

2) OR the missing term and its complement with the original OR term.

X + Y’ à X + Y’ + Z * Z’ = (X + Y’ + Z) (X + Y’ + Z’)

Notes: Z * Z’ = 0

3) Expand the term by applying the distributive property.

Examples

P = ab’ + ac’ + bc

= ab’(c + c’) + a(b + b’)c’ + (a + a’)bc

= ab’c + ab’c’ + abc’ + ab’c’ + abc + a’bc

= ab’c + ab’c’ + abc’ + abc + a’bc

G = f(w, x, y, z) = w’x + yz’

= w’x (y + y’)(z + z’) + (w + w’)(x + x’)yz’

T = f(a,b,c) = (a + b’)(b’ + c)

= (a + b’ + cc’)(b’ + c + aa’)

= (a + b’ + c)(a + b’ + c’)(a + b’ + c)(a’ + b’ + c)

= (a + b’ + c) + (a + b’ +c’) + (a’ + b’ + c)