Logic Gates PDF

System Software and Computing Concepts CT123-3-1Ver: VDE Logic Gates  Topics we will cover Types of Gates Boolean algebra Truth Tables...

System Software and Computing Concepts CT123-3-1Ver: VDE Logic Gates  Topics we will cover Types of Gates Boolean algebra Truth Tables Logic Gate Design Module Code & Module Title Slide Title SLIDE 2  Learning Outcomes At the end of this section, YOU should be able to: Define logic gates Discuss the characteristics of logic gates Explain functions of the AND, OR, NAND, NOR and Exclusive OR gates Design Circuits using Logic Gates Define Boolean Equations and Draw Truth Tables Module Code & Module Title Slide Title SLIDE 3  Key Terms Integrated Circuit Switching Circuit Logic Gate Transistor Resistor Capacitor Karnaugh Map Truth-Table Boolean Module Code & Module Title Slide Title SLIDE 4  Introduction simple collection of digital switches. Computer – -- Computers are built up of Integrated circuits (ICs) ICs are designed for specialized functions – Examples: the CPU, bus interface, memory management unit – Made up of transistors, resistors, capacitors and other electronic components Transistors: primary components of ICs It is possible to fit 6.5 million transistors in less than ½ in 2 Module Code & Module Title Slide Title SLIDE 5  Transistors Transistors are devices that control the movement of electrons, and consequently, electricity. They work something like a water faucet, not only do they start and stop the flow of a current, but they also control the amount of the current. It is the gate part of logic gates One is input , middle is control pin, last is output pin It is essenaitlly a device which controls the flow of electricity can be open or closed via the fact that 1st is input and last is output so if first connected to battery the electricity has ot go through the second one to get to the output, now if we send a closed current through the second one then the gate is closed and no electricity moves Module Code & Module Title Slide Title SLIDE 6  The bigger the resistor the less current , so this controls the amount of voltage that moves, used to control and Resistors & Capacitorsprotect devices capacitors, which are basically batteries. They store electrical current for a very, very short duration of time to allow these components to actually operate. Resistor Capacitor Module Code & Module Title Slide Title SLIDE 7  Motherboard , the black blocks are made up of transistors capacitors and resistors, these are integrated circuits, so are essentially our logic gate components all of em contain but the circles especially are capacitors, all are electronic integrated circuits Module Code & Module Title Slide Title SLIDE 8  Logic Noun Reasoning conducted or assessed according to strict principles of validity: "experience is a better guide to this than deductive logic". A system or set of principles underlying the arrangements of elements in a computer or electronic device so as to perform a specified task. A particular system or codification of the principles of proof and inference: "Aristotelian logic". Synonyms: reason Aristotle Father of Logic Module Code & Module Title Slide Title SLIDE 9  Algebra Boolean algebra: basis for computer logic design Transistors: means for implementing Boolean algebra Switches: on/off to represent the 0’s and 1’s of binary digital circuits Combined to form logic gates Al-Khwarizm: Father of Algebra Module Code & Module Title Slide Title SLIDE 10  note In this car there is this mother board which will have a certain logic concept to it , it has the battery (power source) and wires which connect to each motor, the logic concept of it would contain the instruction set which is on the next slide Module Code & Module Title Slide Title SLIDE 11  This is the instruction set and How it would be used to make This car go onto this path , blue Is the movement and red is the no of the movement we can invoke those behaviours simply by controlling the flow of electricity in this toy car. So by invoking these electrical circuits, these switches we can get the car to behave in a particular action Module Code & Module Title Slide Title SLIDE 12  Digital Circuits Combinatorial logic – Results of an operation depend only on the present inputs to the operation – Uses: perform arithmetic, control data movement, compare values for decision making Sequential logic – Results depend on both the inputs to the operation and the result of the previous operation – Uses: counter Module Code & Module Title Slide Title SLIDE 13  Boolean Algebra Rules that govern constants and variables that can take on 2 values – True/false; on/off; yes/no; 0/1 Boolean logic – Rules for handling Boolean constants and variables – 3 fundamental operations: AND, OR and NOT – Truth Table: specifies results for all possible input combinations Module Code & Module Title Slide Title SLIDE 14  gates All gates are switches. They are the electrical components or the integrated circuits that help us control the flow of that electricity. So if I use an or gate, it will control the flow of electricity. It's a gate. depending on what the signal on A and the signal on B is. Will evaluate what will be on X. And it will then allow maybe turn on or turn off allow the electrical current to flow. Or to block it off to send it an on signal or an off signal , so these can be used as the simple building blocks of programs. The pic bottom right is the one for adding, gates can also be used to store data Module Code & Module Title Slide Title SLIDE 15  Boolean Operators AND A B C – Result TRUE if and only if 0 0 0 both input operands are true 0 1 0 –C=A B 1 0 0 1 1 1 INCLUSIVE-OR A B C An or gate can have more – Result TRUE if any input 0 0 0 than 2 input but is minimum operands are true 2 , if 3 then if 1 is yes then –C=A+B 0 1 1 overall is yes same same, it 1 0 1 takes the + sign , its not adding its js what we use to 1 1 1 represent or Module Code & Module Title Slide Title SLIDE 16  Boolean Operators NOT A C – Result TRUE if single input 0 1 value is FALSE 1 0 –C=A Module Code & Module Title Slide Title SLIDE 17  Boolean Operators EXCLUSIVE-OR A B C – Result TRUE if either A or B is 0 0 0 TRUE but not both 0 1 1 –C=A⊕B 1 0 1 – Can be derived from 1 1 0 INCLUSIVE-OR, AND and NOT A ⊕ B = (A + B)  ( A  B ) A xor B equals A or B but not both A and B A ⊕ B = (A  B ) + ( B  A ) A xor B = either A and not B or B and not A Module Code & Module Title Slide Title SLIDE 18  In a calculator it would contain sm like this, it is a program The c means carry and s means sum , it can only do single digit operations the 4 shown, down left is 0 +0 and down right is 1+1 S1-19 Module Code & Module Title Slide Title SLIDE 19  Boolean Algebra Operations Valid for INCLUSIVE-OR, AND, XOR – Associative A + ( B + C ) = ( A + B ) + C – Distributive A  ( B + C ) = A  B +A  C – Commutative A + B =B + A DeMorgan’s Theorems – A + B =A  B – A  B =A + B Module Code & Module Title Slide Title SLIDE 20  Gates and Combinatorial Logic Many computer functions defined in terms of Boolean equations – Example: sum of 2 single binary digit numbers – Truth table for sum Truth table for carry XOR AND A B C A B C 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 Module Code & Module Title Slide Title SLIDE 21  Computer Implementation Gates or logical gates – Integrated circuits constructed from transistor switches and other electronic components – VLSI: very large-scale integration Module Code & Module Title Slide Title SLIDE 22  Boolean Algebra Implementation Single type of gate appropriately combined 2 possibilities – NAND gate: AND operation followed by a NOT operation This is the XOR truth table and – NOR gate: INCLUSIVE-OR followed by a NOT the plus circle sign for it operation – The truth tables for the nor and nand are js the opp of what the or and add would be Note:  indicates a NOT operation Module Code & Module Title Slide Title SLIDE 23  Selector or Multiplexer In electronics, a multiplexer is a device that selects one of several analog or digital input signals and forwards the selected input into a single line Multiplexers are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth Also called a data selector Module Code & Module Title Slide Title SLIDE 24  Half-Adder Module Code & Module Title Slide Title SLIDE 25  Full Adder Handles possible carry from previous bit – Half adder shown as block to simplify (portion of half adder in Fig. S1.11 enclosed in dotted line) – 2-bit adder contains 32 circuits – Also called ripple adder because the carry ripples through 32 bits Module Code & Module Title Slide Title SLIDE 26  Sequential Logic Circuits Output depends on – Input – Previous state of the circuit Flip-flop: basic memory element State table: output for all combinations of input and previous states Sequential logic is used to construct finite state machines, a basic building block in all digital circuitry, as well as memory circuits and other devices. Module Code & Module Title Slide Title SLIDE 27  Flip-Flop Types with State Tables Module Code & Module Title Slide Title SLIDE 28  Register COPY Operation Uses both sequential and combinatorial logic Module Code & Module Title Slide Title SLIDE 29  Steps in a LOAD Instruction Module Code & Module Title Slide Title SLIDE 30  Example 1. Draw the truth table and write the Boolean Equation Inputs Outputs A B C D E Q 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 2. Draw a circuit that takes input 1 0 0 0 0 0 from 3 doors and raises an alarm whenever all 3 doors are 1 0 1 0 0 0 open. 1 1 0 0 0 0 1 1 1 0 1 1 Module Code & Module Title Slide Title SLIDE 31  Quick Review Questions Draw a circuit that takes input from 2 doors and raises an alarm whenever any door is open. Draw a circuit that takes input from 3 doors and raises an alarm whenever any 2 doors are open Module Code & Module Title Slide Title SLIDE 32  Quick Review Questions Draw the truth table and write the Boolean Equation Module Code & Module Title Slide Title SLIDE 33  Summary Logic functions provide ways to combine different digital signals or signals that can only take one of two possible levels, low level (0) and high level (1), based on the laws of Boolean algebra. These laws are applied using logic gates, which can be classified according to the number of available inputs. In a three‐state buffer, an enable signal is used to control whether the input signal is transferred toward the output or isolated from the output, which is then held in a high‐ impedance state. A logic function can take four states: 0, 1, x and ‐. A function with n variables may be represented by a truth table having n *#x002B; 1 columns and a maximum of 2 n lines. The design of multi‐level circuits is based on the factorization and decomposition of logic functions which are taken in their minimal form. Module Code & Module Title Slide Title SLIDE 34  END Q&A Module Code & Module Title Slide Title SLIDE 35  Next CPU & Memory Module Code & Module Title Slide Title SLIDE 36  example First name all of the gates, second name all of the junctions and the input and output then do final eq and then do truth tabe Module Code & Module Title Slide Title SLIDE 37 Module Code & Module Title Slide Title SLIDE 38