SFU - CMPT 150 - Lectures - Week 4

# SFU - CMPT 150 - Lectures - Week 4 - c A.H.Dixon CMPT 150...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: c A.H.Dixon CMPT 150: Week 4 (Jan 28 - Feb 1, 2008) 26 10 PRODUCT OF MAXTERMS CANONICAL FORM For each row of the function table where the value of the function is 0, construct a sum term with the property that all variables are included, and the value of the sum term is 0 for the assign of values to the variables indicated in the row. Example: x y z f sum term x + y + z 1 x + y + z 1 x + y + z 1 1 1 1 x + y + z 1 1 1 1 1 1 1 1 1 1 Then the expression: ( x + y + z )( x + y + z )(( x + y + z )( x + y + z ) is 0 only when any one of the sum-terms is 0. Therefore it must have the same truth table as the function f . That is, f ( x,y,z ) = ( x + y + z )( x + y + z )(( x + y + z )( x + y + z ) Since all variables occur as literals in each sum term, each is a called a max- term of the function f , and therefore the expression defines f as a product of maxterms. Like the sum of minterms, the product of maxterms representation is also a canon- ical form, and a notation system exists to represent it ”numerically” similar to the Σ notation. In this case we list all the rows in which the function is 0, in a notation called the Π Notation, with the understanding that corresponding maxterms will be ”anded” together: f ( x,y,z ) = Π M (0 , 1 , 2 , 4) Just as every function has a least one sum-of-products representation, so every function has at least one product-of-sums representation. Other product-of-sums c A.H.Dixon CMPT 150: Week 4 (Jan 28 - Feb 1, 2008) 27 representations can be found by applying the distributive, identity, and comple- ment laws in a manner similar to the simplification of sums-of-products. For example, consider the following function: f ( x,y,z ) = Π M (0 , 1 , 2 , 7) = ( x + y + z )( x + y + z )( x + y + z )( x + y + z ) = ( x + y + z )( x +...
View Full Document

{[ snackBarMessage ]}

### Page1 / 5

SFU - CMPT 150 - Lectures - Week 4 - c A.H.Dixon CMPT 150...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online