Basic Logic Operations and Standard Logic Gates [Lecture:1] Instructor: Sajib Roy Lecturer, ETE, ULAB ETE 204 – Digital Electronics

Summer 2012ETE Digital Electronics2 What is an analog signal?

3 Analog Signal An analog signal is a signal that can take on a continuous range of values. Summer 2012ETE Digital Electronics

4 Analog Signal Most, if not all, physical (naturally occurring) quantities are analog values.  Time  Temperature  Pressure Summer 2012ETE Digital Electronics

5 What is an digital signal? Summer 2012ETE Digital Electronics

6 Digital Signal An digital signal is a signal that can take on only discrete (specific) values. Summer 2012ETE Digital Electronics

7 What is an binary signal? Summer 2012ETE Digital Electronics

8 Binary Signal An binary signal is a signal that can take on only two values.  Typically represented by 0 and 1. Summer 2012ETE Digital Electronics

9 Can a binary number be used to represent an analog value? What about accuracy (or is it precision)? Summer 2012ETE Digital Electronics

10 Can a binary number be used to represent an digital value? How many bits are required? Summer 2012ETE Digital Electronics

11 Processing Physical Quantities The analog signal (representing the physical quantity) must be sampled at specific instances in time. The sampled values must be digitized. The digital value must be encoded in binary. Sample and Hold ADC Binary Encoder analog sampleddigitalbinary Summer 2012ETE Digital Electronics

12 Basic Logic Operations Summer 2012ETE Digital Electronics

13 AND Definition: the output is true (1) if both inputs are true (1). F = A.B = AB = “A and B” Boolean expression logical operator ABA. B Truth table F Symbol (aka. logic gate) Summer 2012ETE Digital Electronics

14 OR Definition: the output is true (1) if either or both inputs are true (1). F = A+B = “A or B” Boolean expression logical operator ABA + B Truth table Symbol F F Summer 2012ETE Digital Electronics

15 NOT Definition: the output is true (1) if the input is false (0). F = A' = “ not A” Boolean expression logical operator AA' Truth table Symbol A F = A' Summer 2012ETE Digital Electronics

16 Order of Precedence The order of precedence of the basic logic operations is defined as follows: – NOT – AND – OR The order of precedence can be modified by using parenthesis. Summer 2012ETE Digital Electronics

17 Functionally Complete The AND, OR, and NOT operations comprise a functionally complete set. All logic functions can be expressed in terms of these logic operations. All logic circuits can be realized using the associated logic gates. Summer 2012ETE Digital Electronics

18 NAND Definition: the output is false (0) iff both inputs are true (1). F = (A.B)' = “not (A and B)” Boolean expression AB(A. B)' Truth table F = (A.B)' Symbol shorthand for inversion Summer 2012ETE Digital Electronics

19 NOR Definition: the output is false (0) if either or both inputs are true (1). F = (A+B)' = “not (A or B)” Boolean expression AB(A+B)' Truth table Symbol F F F F = (A+B)' shorthand for inversion Summer 2012ETE Digital Electronics

20 XOR Definition: the output is true (1) if either but not both inputs are true (1). F = A xor B Boolean expression ABA xor B Truth table Symbol logical operator Summer 2012ETE Digital Electronics

21 XNOR (aka. Equivalence) Definition: the output is false (0) if either but not both inputs are true (1). F = A xnor B Boolean expression ABA xnor B Truth table Symbol logical operator Summer 2012ETE Digital Electronics

22 Logic Circuits Logic circuits are realized through the interconnection of logic gates.  Each logic gate represents a logical operation. This can be done using  discrete components Standard Logic Gates  programmable devices Read-only Memories (ROM) Programmable Logic Devices (PLD) Field Programmable Gate Arrays (FPGA) Summer 2012ETE Digital Electronics

23 Standard Logic Gates Summer 2012ETE Digital Electronics

24 Standard Logic Gates DeviceLogic Gate 74xx08 Quad 2-input AND gate 74xx32 Quad 2-input OR gate 74xx04 Hex Inverter (NOT gate) 74xx00 Quad 2-input NAND gate 74xx02 Quad 2-input NOR gate 74xx86 Quad 2-input XOR gate Note: “xx” refers to the logic family Summer 2012ETE Digital Electronics

25 Standard Logic Gates Data sheets provide essential information:  Logic Function  Truth Table  Pin-out  Electrical Characteristics  Timing Characteristics  Package Description(s) This information is necessary when building logic circuits from discrete components. Each logic family has a unique set of characteristics. Summer 2012ETE Digital Electronics

ECE Digital Electronics26 Standard Logic Gates: 74xx08 pin-out Truth table Summer 2012ETE Digital Electronics

ECE Digital Electronics27 Standard Logic Gates: 74xx32 pin-out Truth table Summer 2012ETE Digital Electronics

ECE Digital Electronics28 Standard Logic Gates: 74xx04 pin-out Truth table Summer 2012ETE Digital Electronics

29 Building a Logic Circuit Circuit Diagram B C A F inputsoutput F = B'.C + A.B Boolean Expression 74xx08 74xx32 74xx04 Summer 2012ETE Digital Electronics

30 Building a Logic Circuit components wires inputs output Wiring Diagram Summer 2012ETE Digital Electronics

31 Draw the circuit diagram and wiring diagram for the following Boolean expression: F = A'.B + A.B' Example Summer 2012ETE Digital Electronics

32 Example (circuit diagram) Summer 2012ETE Digital Electronics

33 Example Summer 2012ETE Digital Electronics

34 Questions? Summer 2012ETE Digital Electronics