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Appendix A Logic Circuits

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Logic circuits Operate on binary variables that assume one of two distinct values, usually called 0 and 1 Implement functions of logic variables Circuits have inputs and outputs Circuits are implemented using electronic logic gates

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Standard logic gate symbols

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Implementation of the XOR function using AND, OR, and NOT gates

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Synthesis of logic functions Synthesis is the process of designing and implementing a logic circuit defined by its functional specification. The expression for f in the previous circuit is said to be in a sum-of-products form, because the OR and AND operations are sometimes called the sum and product functions.

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Implementation of a logic function

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Proving equivalence of expressions

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Rules of binary logic

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Minimization of logic expressions As illustrated in the previous example, a logic function can be implemented with circuits of different complexities. It is useful to minimize a logic expression to reduce the cost of the synthesized circuit.

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Three-variable Karnaugh maps

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Four-variable Karnaugh maps

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Using don’t cares

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NAND and NOR gates

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Equivalence of NAND-NAND and AND-OR networks

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Cascading of gates

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Representation of logic values by voltage levels

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Tri-state buffer

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A basic latch implemented with NOR gates

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Gated SR latch

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Gated SR latch implemented with NAND gates

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Gated D latch

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Master-slave D flip-flop

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A negative-edge-triggered D flip-flop

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T flip-flop

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JK flip-flop

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Master-slave D flip-flop with Preset and Clear

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Shift register

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Parallel-access shift register

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A 3-bit up-counter

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A two-input to four-output decoder

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A BCD-to-7-segment display decoder

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A four-input multiplexer

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Multiplexer implementation of a logic function

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A block diagram for a PLD

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Functional structure of a PLA

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A simplified sketch of the previous PLA

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An example of a PAL

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Inclusion of a flip-flop in a PAL element

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Organization of a CPLD

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A conceptual block diagram of an FPGA

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Sequential circuits A logic circuit whose output is determined entirely by its present inputs is called a combinational circuit (e.g. decoders and multiplexers). A logic circuit whose output depends on both the present inputs and the state of the circuit is called a sequential circuit (e.g. counters).

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State diagram of a mod-4 up/down counter that detects the count of 2

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State table

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State assignment table

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The next-state expressions are: The output expression is

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Implementation of the up/down counter

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Timing diagram for the designed counter

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A formal model of a finite state machine

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