Logic Gates: System Software and Computing Concepts 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. Module Code & Module Title Slide Title SLIDE 6  Resistors & Capacitors Capacitor Resistor Module Code & Module Title Slide Title SLIDE 7  Motherboard 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  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 11  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 12  Boolean Operators AND A B C – Result TRUE if and only if both 0 0 0 input operands are true 0 1 0 –C=A B 1 0 0 1 1 1 INCLUSIVE-OR – Result TRUE if any input A B C operands are true 0 0 0 –C=A+B 0 1 1 1 0 1 1 1 1 Module Code & Module Title Slide Title SLIDE 13  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 14  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 15  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 16  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 17  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 18  Boolean Algebra Implementation Single type of gate appropriately combined 2 possibilities – NAND gate: AND operation followed by a NOT operation – NOR gate: INCLUSIVE-OR followed by a NOT operation Note:  indicates a NOT operation Module Code & Module Title Slide Title SLIDE 19  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 20  Half-Adder Module Code & Module Title Slide Title SLIDE 21  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 22  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 23  Flip-Flop Types with State Tables Module Code & Module Title Slide Title SLIDE 24  Register COPY Operation Uses both sequential and combinatorial logic Module Code & Module Title Slide Title SLIDE 25  Steps in a LOAD Instruction Module Code & Module Title Slide Title SLIDE 26  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 27  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 28  Quick Review Questions Draw the truth table and write the Boolean Equation Module Code & Module Title Slide Title SLIDE 29  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 30  END Q&A Module Code & Module Title Slide Title SLIDE 31  Next CPU & Memory Module Code & Module Title Slide Title SLIDE 32