CPS120: Introduction to Computer Science

Slides:



Advertisements
Similar presentations
Chapter 4 Gates and Circuits.
Advertisements

Chapter 4 Gates and Circuits Nell Dale • John Lewis.
Chapter 4 Gates and Circuits.
Gates and Circuits Nell Dale & John Lewis (adaptation by Erin Chambers and Michael Goldwasser)
CS105 Introduction to Computer Concepts GATES and CIRCUITS
Chapter 4 Gates and Circuits.
Chapter 4 Gates and Circuits.
Chapter 4 Gates and Circuits.
9/19/06 Hofstra University – Overview of Computer Science, CSC005 1 Chapter 4 Gates and Circuits.
9/19/06 Hofstra University – Overview of Computer Science, CSC005 1 Chapter 4 Gates and Circuits.
Informationsteknologi Friday, October 19, 2007Computer Architecture I - Class 81 Today’s class Digital Logic.
TDC 311 Digital Logic. Truth Tables  AND  OR  NOT  NAND  NOR  XOR  XNOR.
Lecture 3. Boolean Algebra, Logic Gates
Gates A digital circuit is one in which only two logical values are present. Typically, a signal between 0 and 1 volt represents one value (e.g. binary.
Any logic circuits can be transformed to an implementation where only NAND gates (and inverters) are used. The general approach to finding a NAND-gate.
Part 2: DESIGN CIRCUIT. LOGIC CIRCUIT DESIGN x y z F F = x + y’z x y z F Truth Table Boolean Function.
Lecture 3. Boolean Algebra, Logic Gates Prof. Sin-Min Lee Department of Computer Science 2x.
Chapter 4 Gates and Circuits. 4–2 Chapter Goals Identify the basic gates and describe the behavior of each Describe how gates are implemented using transistors.
Chapter 4 Gates and Circuits.
Lecture 3. Error Detection and Correction, Logic Gates Prof. Sin-Min Lee Department of Computer Science 2x.
Quiz # 2 Chapters 4, 5, & 6.
Chapter 4 Gates and Circuits. Integrated Circuits aka CHIPS What’s in this thing???? 4–2.
Chapter 4 Gates and Circuits.
Digital Computer Concept and Practice Copyright ©2012 by Jaejin Lee Logic Circuits I.
Fundamentals of IT UNIT-I OnlyforIPMCA. DIGITAL SIGNALS & LOGIC GATES Signals and data are classified as analog or digital. Analog refers to something.
Digital Components and Combinational Circuits Sachin Kharady.
The Digital Logic Level
Digital Computer Concept and Practice Copyright ©2012 by Jaejin Lee Logic Circuits I.
1 DIGITAL ELECTRONICS. 2 OVERVIEW –electronic circuits capable of carrying out logical (boolean) and arithmetic operations on information stored as binary.
1 Boolean Algebra & Logic Gates. 2 Objectives Understand the relationship between Boolean logic and digital computer circuits. Learn how to design simple.
Multiplexers 1 The output is equal to one of several input signals to the circuit The multiplexer selects which input signal to use as an output signal.
Adders Half-adder  Adds two bits Produces a sum and carry  Problem: Cannot use it to build larger inputs Full-adder  Adds three 1-bit values Like half-adder,
Week 6: Gates and Circuits: PART I READING: Chapter 4.
Sneha.  Gates Gates  Characteristics of gates Characteristics of gates  Basic Gates Basic Gates  AND Gate AND Gate  OR gate OR gate  NOT gate NOT.
Logic Design CS 270: Mathematical Foundations of Computer Science Jeremy Johnson.
1 EG 32 Digital Electronics Thought for the day You learn from your mistakes..... So make as many as you can and you will eventually know everything.
Magnitude Comparator Dr. Ahmed Telba.
Digital electronics 4–1 Gates and Circuits SANJAYBHAI RAJGURU COLLEGE OF ENGG.
Logic Gates Dr.Ahmed Bayoumi Dr.Shady Elmashad. Objectives  Identify the basic gates and describe the behavior of each  Combine basic gates into circuits.
4–1. BSCS 5 th Semester Introduction Logic diagram: a graphical representation of a circuit –Each type of gate is represented by a specific graphical.
LOGIC CIRCUITLOGIC CIRCUIT. Goal To understand how digital a computer can work, at the lowest level. To understand what is possible and the limitations.
L OGIC G ATES Computer Organization – week 3. W HAT ’ S ALU? 1. ALU stands for: Arithmetic Logic Unit 2. ALU is a digital circuit that performs Arithmetic.
4–1 Gates Let’s examine the processing of the following six types of gates NOT AND OR XOR NAND NOR Typically, logic diagrams are black and white, and the.
Week 1: Introduction and Logic gates IT3002 – Computer Architecture
Basics of Logic gates - Part 2
Basics of Logic gates - Part 1
Dr.Ahmed Bayoumi Dr.Shady Elmashad
Chapter 3 - Binary Numbering System
Dr.Ahmed Bayoumi Dr.Shady Elmashad
CSIS-110 Introduction to Computer Science
CS140 Lecture 03: The Machinery of Computation: Combinational Logic
Fundamentals & Ethics of Information Systems IS 201
NAND-ONLY LOGIC CIRCUITS
Basics Combinational Circuits Sequential Circuits
Basics Combinational Circuits Sequential Circuits Ahmad Jawdat
Chapter 4 Gates and Circuits.
CS105 Introduction to Computer Concepts GATES and CIRCUITS
Agenda – 2/12/18 Questions? Readings: CSI 4, P
Boolean Algebra.
Week 7: Gates and Circuits: PART II
Digital Logic.
Logic Gates.
Computer Organization
DIGITAL ELECTRONICS B.SC FY
Chapter 4 Gates and Circuits.
XOR, XNOR, and Binary Adders
XOR Function Logic Symbol  Description  Truth Table 
Department of Electronics
Digital Logic Design Basics Combinational Circuits Sequential Circuits.
What are Logic Gates?.
Presentation transcript:

CPS120: Introduction to Computer Science Gates and Circuits Nell Dale • John Lewis

Computers and Electricity A gate is a device that performs a basic operation on electrical signals Gates are combined into circuits to perform more complicated tasks

Computers and Electricity There are three different, but equally powerful, notational methods for describing the behavior of gates and circuits Boolean expressions logic diagrams truth tables

Computers and Electricity Boolean algebra: expressions in this algebraic notation are an elegant and powerful way to demonstrate the activity of electrical circuits

Computers and Electricity Logic diagram: a graphical representation of a circuit Each type of gate is represented by a specific graphical symbol Truth table: defines the function of a gate by listing all possible input combinations that the gate could encounter, and the corresponding output

Gates Let’s examine the processing of the following six types of gates NOT AND OR XOR NAND NOR Typically, logic diagrams are black and white, and the gates are distinguished only by their shape

NOT Gate A NOT gate accepts one input value and produces one output value

NOT Gate By definition, if the input value for a NOT gate is 0, the output value is 1, and if the input value is 1, the output is 0 A NOT gate is sometimes referred to as an inverter because it inverts the input value

AND Gate An AND gate accepts two input signals If the two input values for an AND gate are both 1, the output is 1; otherwise, the output is 0

OR Gate If the two input values are both 0, the output value is 0; otherwise, the output is 1

XOR Gate XOR, or exclusive OR, gate An XOR gate produces 0 if its two inputs are the same, and a 1 otherwise Note the difference between the XOR gate and the OR gate; they differ only in one input situation When both input signals are 1, the OR gate produces a 1 and the XOR produces a 0

XOR Gate

NAND and NOR Gates The NAND and NOR gates are essentially the opposite of the AND and OR gates, respectively Various representations of a NAND gate Various representations of a NOR gate

Review of Gate Processing A NOT gate inverts its single input value An AND gate produces 1 if both input values are 1 An OR gate produces 1 if one or the other or both input values are 1

Review of Gate Processing (cont.) An XOR gate produces 1 if one or the other (but not both) input values are 1 A NAND gate produces the opposite results of an AND gate A NOR gate produces the opposite results of an OR gate

Gates with More Inputs Gates can be designed to accept three or more input values A three-input AND gate, for example, produces an output of 1 only if all input values are 1 Various representations of a three-input AND gate

Circuits Two general categories In a combinational circuit, the input values explicitly determine the output In a sequential circuit, the output is a function of the input values as well as the existing state of the circuit As with gates, we can describe the operations of entire circuits using three notations Boolean expressions logic diagrams truth tables

Combinational Circuits Gates are combined into circuits by using the output of one gate as the input for another

Combinational Circuits Because there are three inputs to this circuit, eight rows are required to describe all possible input combinations This same circuit using Boolean algebra: (AB + AC)

Properties of Boolean Algebra

Adders At the digital logic level, addition is performed in binary Addition operations are carried out by special circuits called, appropriately, adders

Adders The result of adding two binary digits could produce a carry value Recall that 1 + 1 = 10 in base two A circuit that computes the sum of two bits and produces the correct carry bit is called a half adder

Adders sum = A  B carry = AB Circuit diagram representing a half adder Two Boolean expressions: sum = A  B carry = AB Page 103

Adders A circuit called a full adder takes the carry-in value into account A full adder

Multiplexers Multiplexer is a general circuit that produces a single output signal The output is equal to one of several input signals to the circuit The multiplexer selects which input signal is used as an output signal based on the value represented by a few more input signals, called select signals or select control lines

Multiplexers The control lines S0, S1, and S2 determine which of eight other input lines (D0 through D7) are routed to the output (F) A block diagram of a multiplexer with three select control lines

Circuits as Memory Digital circuits can be used to store information These circuits form a sequential circuit, because the output of the circuit is also used as input to the circuit

Circuits as Memory An S-R latch stores a single binary digit (1 or 0) There are several ways an S-R latch circuit could be designed using various kinds of gates An S-R latch

Circuits as Memory The design of this circuit guarantees that the two outputs X and Y are always complements of each other The value of X at any point in time is considered to be the current state of the circuit Therefore, if X is 1, the circuit is storing a 1; if X is 0, the circuit is storing a 0 An S-R latch

Integrated Circuits An integrated circuit (also called a chip) is a piece of silicon on which multiple gates have been embedded These silicon pieces are mounted on a plastic or ceramic package with pins along the edges that can be soldered onto circuit boards or inserted into appropriate sockets

Integrated Circuits Integrated circuits (IC) are classified by the number of gates contained in them

Integrated Circuits TTL An SSI chip contains independent NAND gates

CPU Chips The most important integrated circuit in any computer is the Central Processing Unit, or CPU Each CPU chip has a large number of pins through which essentially all communication in a computer system occurs