4.1 Swithcing Algebra

4.1 Swithcing Algebra - Analysis and Synthesis: Analysis...

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Unformatted text preview: Analysis and Synthesis: Analysis start with a logic diagram and proceed to a formal description of the function performed by that circuit, such as a truth table or a logic expression. 4.1 Switching Algebra Return Next 1. Introduction Logic circuits are classified into two types: Combinational: whose outputs depend only on its current inputs. Sequential: depend not only on the current inputs but also on the past sequence of inputs, possibly arbitrarily far back in time. 4.1 Switching Algebra Next Back Return Synthesis do the reverse, starting with a formal description and proceeding to a logic diagram. 2. Axioms 1+0=0+1=1 A5’ · 1=1 · 0=0 A5 0+0=0 A4’ 1 · 1=1 A4 1+1=1 A3’ · 0=0 A3 if x=1, then x=0 A2’ if x=0, then x=1 A2 x=1 if x≠0 A1’ x=0 if x≠1 A1 4.1 Switching Algebra Next Back Return 3. Theorems with One Variable x · x=0 T5’ x+x=1 T5 T4’ x =x T4 x · x=x T3’ x+x=x T3 x · 0=0 T2’ x+1=1 T2 x · 1=x T1’ x+0=x T1 Identities Null elements Idempotency Complements Involution 4.1 Switching Algebra Next Back Return 4. Theorems with multi-variable I x · y+x · z=x · (y+z) T8 (x+y)+z=x+(y+z) T7 x+y=y+x T6 (x+y) · (x+z)=x+y · z T8’ (x · y) · z=x · (y · z) T7’ x · y=y · x T6’ Commutativity Associativity Distributivity 4.14....
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This note was uploaded on 03/16/2010 for the course CSE 2300W taught by Professor Shi during the Fall '08 term at UConn.

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4.1 Swithcing Algebra - Analysis and Synthesis: Analysis...

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