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Combinational Logic Analysis

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Basic Combinational Logic Circuits AND-OR logic AND-OR logic AND-OR logic produces an SOP expression. AND-OR logic produces an SOP expression. In general, an AND- OR circuit can have any number of AND gates each with any number of inputs. In general, an AND- OR circuit can have any number of AND gates each with any number of inputs. A B C D AB CD X=AB+CD SOP

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Basic Combinational Logic Circuits A B C D AB CD X=AB+CD inputsABCDo/pABCDX 0000000 0001000 0010000 0011011 0100000 0101000 0110000 0111011 1000000 1001000 1010000 1011011 1100101 1101101 1110101 1111111

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Basic Combinational Logic Circuits AND-OR-Invert logic AND-OR-Invert logic A B C D AB CD AB+CD X=AB+CD POS

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XOR Basic Combinational Logic Circuits Exclusive-OR logic Exclusive-OR logic Inputs X AB 000 011 101 110 A B

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Basic Combinational Logic Circuits Exclusive-NOR logic Exclusive-NOR logic A B XOR X A B X

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Implementing Combinational Logic Boolean expression logic circuit Boolean expression logic circuit For every Boolean expression there is a logic circuit, and for every logic circuit there is a Boolean expression For every Boolean expression there is a logic circuit, and for every logic circuit there is a Boolean expression What’s the benefit? >> Less overall propagation delay > Less overall propagation delay <<

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Implementing Combinational Logic

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Truth table logic circuit Truth table logic circuit If you begin with a truth table of an expression, you can write the SOP expression from the truth table and then implement the logic circuit. If you begin with a truth table of an expression, you can write the SOP expression from the truth table and then implement the logic circuit. Remember? SOP AND-OR implementation. Remember? SOP AND-OR implementation.

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Truth table logic circuit

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Minimizing Logic & Implementation

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Universal Gates The NAND gate The NAND gate

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Universal Gates The NOR gate The NOR gate

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Logic Circuit Operation with Pulse How can we deal with combinational logic circuits with pulse waveform inputs? How can we deal with combinational logic circuits with pulse waveform inputs? The operation of each gate is the same for pulse waveform inputs as for constant-level inputs. The operation of each gate is the same for pulse waveform inputs as for constant-level inputs. The output of a logic circuit at any given time depends on the inputs at that particular time, so the relationship of the time-varying inputs is of primary importance. The output of a logic circuit at any given time depends on the inputs at that particular time, so the relationship of the time-varying inputs is of primary importance.

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Logic Circuit Operation with Pulse Let’s get to the basic with a given individual gate: Let’s get to the basic with a given individual gate:

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Logic Circuit Operation with Pulse

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