# l08 - Combinational Logic Multiple levels of representation...

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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: Combinational Logic Multiple levels of representation: • Logic equations • Truth tables • Gate diagrams • Switching circuits Boolean algebra: tool to manipulate logic equations An algebra on a set of two elements: { , 1 } Operations: AND, OR, complement Boolean Algebra Identities: a = 0 1 a = a aa = a aa = 0 0 + a = a 1 + a = 1 a + a = a a + a = 1 ab = ba a ( bc ) = ( ab ) c a + b = b + a a + ( b + c ) = ( a + b ) + c a ( b + c ) = ab + ac a + ( bc ) = ( a + b )( a + c ) ( a + b ) = a b ( ab ) = a + b Precedence: AND takes precedence over OR. Proving Logic Equations Example: ( a + b )( a + c ) = a + bc Algebraic proof? Proof with Truth Tables: a b c a + b a + c LHS bc RHS 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Truth Tables To Logic Equations a b c out Minterms Maxterms a b c a + b + c 1 1 a b c a + b + c 1 1 a bc a + b + c 1 1 a bc a + b + c 1 1 ab c a + b + c 1 1 1 ab c a + b + c 1 1 abc a + b + c 1 1 1 abc a + b + c Sum of Products: a b c + a bc + ab c + ab c Product of Sums: ( a + b + c )( a + b + c )( a + b + c )( a + b + c ) Universality: NAND and NOR = = = = Universal: can implement any combinational function using just NAND or just NOR gates. Minimizing Logic Equations...
View Full Document

## This note was uploaded on 06/25/2008 for the course ECE 3140 taught by Professor Mckee/long during the Spring '07 term at Cornell.

### Page1 / 24

l08 - Combinational Logic Multiple levels of representation...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online