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Logic Gates. Transistors as Switches. EB voltage controls whether the transistor conducts in a common base configuraiton. Logic circuits can be built. AND. In order for current to flow, both switches must be closed Logic notation A B = C. OR. Current flows if either switch is closed

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## Logic Gates

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**Transistors as Switches**• EB voltage controls whether the transistor conducts in a common base configuraiton. • Logic circuits can be built**AND**• In order for current to flow, both switches must be closed • Logic notation AB = C**OR**• Current flows if either switch is closed • Logic notation A + B = C**Properties of AND and OR**• Commutation • A + B = B + A • A B = B A Same as Same as**Properties of AND and OR**• Associative Property • A + (B + C) = (A + B) + C • A (B C) = (A B) C =**Properties of AND and OR**• Distributive Property • A + B C = (A + B) (A + C) • A + B C**Distributive Property**• (A + B) (A + C)**Binary Addition**Notice that the carry results are the same as AND C = A B**Inversion (NOT)**Logic:**Exclusive OR (XOR)**Either A or B, but not both This is sometimes called the inequality detector, because the result will be 0 when the inputs are the same and 1 when they are different. The truth table is the same as for S on Binary Addition. S = A B**Getting the XOR**Two ways of getting S = 1**Circuit for XOR**Accumulating our results: Binary addition is the result of XOR plus AND**Half Adder**Called a half adder because we haven’t allowed for any carry bit on input. In elementary addition of numbers, we always need to allow for a carry from one column to the next. 18 25 3 (plus a carry) 4**Chaining the Full Adder**Possible to use the same scheme for subtraction by noting that A – B = A + (-B)**Binary Counting**Use 1 for ON Use 0 for OFF = 00101011 So our example has 25 + 23 + 21 + 20 = 32 + 8 + 2 + 1 = 43 Binary Counter**Exclusive NOR**Equality Detector

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