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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 1 CSE-221 Digital Logic Design (DLD) Lecture-2: Logic Operations & Digital Logic Gates

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 2 Analog: values vary over a broad range continuously Digital: only discrete values +5 V –5 101 Time +5 V –5 Time Analog vs. Digital

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 3 Analog vs. Digital Analog devices process signal that can assume any value across a continuous range and produce results that are also in continuous form. Digital devices process signals that take on only two discrete values such as 0 and 1 and produces output that can be represented by 0 and 1. Examples Analog Devices: solid-state devices TV (except for digital TV), Audio amplifier etc. Digital Devices: Computer, CD player, digital TV, digital cellular phone, electronic calculator, and digital camera.

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 4 Analog systems: Limited precision, errors accumulate, drift Interface circuits (i.e., sensors & actuators) often analog Analog vs. Digital Systems Digital systems: More accurate and reliable Readily available as self-contained, easy to cascade building blocks Computers use digital circuits internally

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 5 AND Operator Let’s look at the relationship between the semantic and logical operator known as the AND operator Consider: If the car is fueled AND the engine works, then the engine will start AND Operator Truth Table 000 ABOutput 010 100 111 AND means that both conditions must be true in order for the conclusion to be true

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 6 Digital AND We can build an electrical device that performs the logical AND operation on voltage equivalents of logic values An AND gate has the electrical schematic: For digital logic: True = 1 is 5 volts False = 0 is 0 volts A Inputs B Output Practice with the Excel spreadsheet Another basic operator is the OR Consider: If I have cash OR a credit card, then I can pay the bill OR works such that the output is true, if either of the two inputs is true OR Operator 000 ABOutput 011 101 111 OR Operator Truth Table

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 7 XOR (Exclusive OR) Operator Let’s look at the relationship between the semantic and logical operator known as the XOR operator Consider a biological example: If gender A XOR gender B, then reproduction is possible XOR works such that output is activated (equal to one) if both inputs are of a different value Try the Excel spreadsheet exercise We can build an electrical device that performs the logical XOR operation on voltage equivalents of logic values An XOR gate has the electrical schematic: 000 ABOutput 011 101 110 A Inputs Output B

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 8 Multi-Input AND Gate AND gates can be built with any number of inputs Consider the symbol for the 4-input AND gate F is true only when all the inputs are true (1’s) Using the Excel workbook “EE-WISE-Digital Lab”, open the “Digital Locks” worksheet, and test this circuit ABCDABCD F All digital computers are built using only three gate types: AND, OR, and NOT

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 9 Digital Combination Lock Using 3 two-input AND gates, we could build a combination lock that requires a four-digit code, specifically: 1 1 1 1 The number of inputs could be increased by using more and more AND gates AND 1 1 1 1 1 1 1

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 10 Digital Combination Lock We could build a combination lock that only uses the AND gate, but that would be of little use since everyone would know our combination, namely 1 1 1 1 To build a more interesting combination lock, we will utilize the NOT (inverter) gate 01 Let’s build a combination lock whose input (key code) combination is 0 1 1 0 Is there any other combination that works? AND 1 1 1 1 1 1 1 0 0

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 11

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6/16/2004P.B-Dr M.A.kashem(CS&E- 221,TLDD2) 12 Each of the functions in Table 2-8 is listed with an accompanying name and a comment that explains the function in some way. The 16 functions listed can be subdivided into three categories: 1) Two functions that produce a constant 0 or 1 2) Four functions with unary operations: complement and transfer. 3) Ten functions with binary operators that define eight different operations. AND, OR, NAND, NOR, exclusive-OR, equivalence, inhibition, and implication.

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