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posttheorems - CS2204 DIGITAL LOGIC STATE MACHINE DESIGN...

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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
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