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Logic Gates A logic gate is an elementary building block of a digital circuit Most logic gates have two inputs and one output At any given moment, every terminal is in one of the two binary conditions low (0) or high (1) represented by different voltage levels The logic state of a terminal can, and generally does, change often, as the circuit processes data In most logic gates, the low state is approximately zero volts (0 V) while the high state is approximately five volts positive (+5 V).

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Truth Tables A truth table shows how a logic circuit's output responds to various combinations of the inputs using logic 1 for true and logic 0 for false. All permutations of the inputs are listed on the left output of the circuit is listed on the right The desired output can be achieved by a combination of logic gates A truth table for two inputs is shown, but it can be extended to any number of inputs. The input columns are usually constructed in the order of binary counting with a number of bits equal to the number of inputs.

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NOT Gate or Inverter The output of a not gate is always opposite to it's input An X with a vertical bar over it means 'NOT X' .

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AND gate An AND gate always has one output, but it can have many inputs (at least 2). The output is high only when both inputs A and B are high.

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**Relay logic equivalent**

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OR gate As with the AND gate, the OR gate has one output and several inputs. X+Y is equivilent to X OR Y. The output is high when either or both of inputs A or B is high. Below we have pictured a 2-input OR gate.

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**Relay logic equivalent**

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NAND gates A NAND gate is equivalent to an AND gate followed by a NOT gate. Notice that the bar stretches over all of the expression, to say that the whole thing is negated The output is high when either of inputs A or B is high, or if neither is high. In other words, it is normally high, going low only if both A and B are high.

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**Relay logic equivalent**

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NOR gates A NOR gate is an OR gate followed by a not gate. Notice that the bar stretches over all of the expression, to say that the whole thing is negated The output is high only when neither A nor B is high. That is, it is normally high but any kind of non-zero input will take it low.

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**Relay logic equivalent**

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EXOR gates EXOR (or EXclusive OR) gives TRUE if either but not both inputs are TRUE Notice that the symbol for EXOR is + (as in OR) in a circle The output is high when either of inputs A or B is high, but not if both A and B are high.

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**Relay logic equivalent**

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**Negative Logic Gates Each of the basic gates has a negative logic**

equivalent as shown. The equivalence is shown by the application of DeMorgan's theorem. It amounts to changing AND's to OR's or vice versa and inverting all inputs.

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A practical operational way to look at DeMorgan's Theorem is that the inversion bar of an expression may be broken at any point and the operation at that point replaced by its opposite (i.e., AND replaced by OR or vice versa

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**Exercise 1 What is the truth table for this circuit?**

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**What is the truth table for this circuit?**

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COFFEE MACHINE

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FLIP FLOP

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Setting the NAND Latch After being set to Q=1 by the low pulse at S (NAND gate function), the restored normal value S=1 is consistent with the Q=1 state, so it is stable. Another negative pulse on S gives which does not switch the flip-flop, so it ignores further input.

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**Resetting the NAND Latch**

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Nor Flip Flop

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1 EENG 2710 Chapter 2 Algebraic Methods For The Analysis and Synthesis of Logic circuits.

1 EENG 2710 Chapter 2 Algebraic Methods For The Analysis and Synthesis of Logic circuits.

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