{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

posttheorems

# posttheorems - CS2204 DIGITAL LOGIC STATE MACHINE DESIGN...

This preview shows pages 1–2. Sign up to view the full content.

MATHEMATICAL FOUNDATION OF DIGITAL CIRCUITS CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN FALL 2009 P olytec hnic Institute of NYU P a g e 1 of 4 Handout No : 4 September 22, 2009 Digital Circuits CS 2204 studies digital circuits. It focuses on the theory , analysis and synthesis (design) of digital circuits. The the- ory provides the mathematical foundation (i) to analyze and design digital circuits, (ii) to verify that a circuit per- forms what it is supposed to and (iii) to simplify (minimize) digital circuits. The analysis means a digital circuit is given and we are asked to determine its input-output relationship (its pur- pose, operation, what it does). One studies a circuit and then states the input-output relationship (the purpose) of the circuit in text or on a truth table or on an operation table or or on a state diagram or on an operation diagram. If the circuit is complex, one needs to employ block-based analysis to obtain the purpose. The synthesis means an input-output relationship (purpose, operation) is given and we are asked to design the digital circuit. One studies the input-output relationship (the purpose) of a circuit which is in text or on an operation table or on an operation diagram and then designs the circuit. If the circuit is complex, one needs to employ block-based design to obtain the digital circuit. It is clear that the input-output relationship is a very crucial element of digital circuit study. Another one is the block- based approach : Complex digital circuits are worked on piece by piece (block by block) to handle the large number of details. Blocks are analyzed/designed individually, then they are combined one by one and analyzed/designed and finally the whole circuit is analyzed/designed. The input-output relationship and block-based approach treat the digital circuit as a black box with inputs and outputs in the beginning. It focuses on the relationship of outputs to its inputs : Every output must be described as a function of its inputs. We know from our experience that a function is a mathematical entity that precisely describes how an output is determined by its inputs. For example, in the figure below, the digital circuit shown as a black box has three inputs and two outputs (two digital functions) : a b c y = f 1 (a, b, c) z = f 2 (a, b, c) Digital Circuit

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.

{[ snackBarMessage ]}