All notes short and easy to learn for a student of electrical engineering, Cheat Sheet of Electrical Engineering

Download All notes short and easy to learn for a student of electrical engineering and more Cheat Sheet Electrical Engineering in PDF only on Docsity! CHAPTER-1 ANALOG SIGNAL  An analog signal is any continuous signal for which the time-varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal.  For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves. Factors Analog Digital Waves Denoted by Sine waves Denoted by Square waves Signal Continuous signal representing physical Discrete signal representing measurements discrete time signals generated by digital modulation Data Transmission Subject to deterioration by noise Noise-immune without deterioration Bandwidth Consumes less bandwidth Consumes more bandwidth Memory Stored in the form of wave signal Stored in the form of binary bit Power Draws large power Draws negligible power Impedance Low impedance High order of 100 megachm Errors Analog instruments have considerable | Digital instruments are free observational errors from observational errors Advantages Of Digital Signal  Easier To Design.  Digital System Have Got Fast Response Time.  Information Can Be Stored And Retrived Very Easily.  More Accurate And Have Great Percision.  Less Effected By Noise.  Easier To Use Because Direct Display Of Data Is Convenient To Read.  Digital Ckt. Can Be Fabricated On IC Chips. Advantages of Analog Signal » Best suited for the transmission of audio and video. » Consume less bandwidth than digital signals to carry the same information. » Analog signal is less susceptible to noise. CHAPTER -2 Number system & its types  Code using symbols that refers to a set of items.  Types of Number system Binary number system Decimal number system Octal number system Hexa -decimal number system Binary Number System  A number system which have two values 0 and 1 is called binary number system.  The base or radix is 2. Example 12510 = ?2 2 125 62 12 31 02 15 12 7 1 2 3 12 1 12 0 1 12510 = 11111012 Binary to Decimal Conversion  Technique  Multiply each bit by 2n, where n is the “weight” of the bit  The weight is the position of the bit, starting from 0 on the right  Add the results Example 1010112 => 1 x 20 = 1 1 x 21 = 2 0 x 22 = 0 1 x 23 = 8 0 x 24 = 0 1 x 25 = 32 4310 Octal to Binary conversion  Technique  Convert each octal digit to a 3-bit equivalent binary representation Example 7058 = ?2 7 0 5 111 000 101 7058 = 1110001012 Binary to Octal  Technique  Group bits in threes, starting on right  Convert to octal digits Example 7248 => 4 x 80 = 4 2 x 81 = 16 7 x 82 = 448 46810 Decimal to Octal  Technique  Divide by 8  Keep track of the remainder Example 123410 = ?8 8 1234 154 28 19 2 8 2 38 0 2 123410 = 23228 Binary to Hexadecimal  Technique  Group bits in fours, starting on right  Convert to hexadecimal digits Example 10101110112 = ?16 10 1011 1011 2 B B 10101110112 = 2BB16 Hexadecimal to Binary  Technique  Convert each hexadecimal digit to a 4-bit equivalent binary representation Example ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560 274810 Binary Addition  The binary number system uses only two digits 0 and 1. So , there are four basic operations. 0+0=0 0+1=1 1+0 = 1 1+1 = 10 Binary Subtraction The subtraction of binary digit depends on four basic operation. 0-0 = 0 1-0 = 1 1 – 1 = 0 10 – 1 = 1 CHAPTER- 3 Binary Codes  Binary codes are used in computers and digital communication. These binary codes can be classified as:  Weighted codes  Non- weighted codes Binary Codes • Electronic digital systems use signals that have two distinct values and circuit elements that have two stable states. • Digital systems represent and manipulate not only binary numbers, but also many other discrete elements of information. • Any discrete element of information distinct among a group of quantities can be represented by a binary code. • Binary codes merely change the symbols, not the meaning of the elements of information that they represent. Non – Weighted Codes  In non-weighted codes, each digit of the code do not have any position weight.  Example of non –weighted codes are: ASCII CODE, Excess -3 code, Gray code. Gray Code Table 2-10 . . Decimal Binary Gray A comparison of 3-bit Number Code Code binary code and Gray code. 0 000 000 1 001 001 2 010 O11 3 O11 010 4 100 110 5 101 111 6 110 101 7 111 100 Excess -3 code • The code word for each decimal digit is the corresponding BCD code word plus 00112.  0010 = 2 in BCD  + 00112  = 0101 = 2 in excess-3 EVEN PARITY  In this method , one extra bit known as parity bit is added to the binary information.  The parity is added in such a way that the total number of one’s becomes even. ODD PARITY  It is similar to even parity method but the total number of one’s should be odd.  Example of Even and Odd parity ——— soe SATS ANE AND Gate  The AND gate implements the Boolean AND function where the output only is logical 1 when all inputs are logical 1.  The standard symbol and the truth tabel for a two input AND gate is: OR Gate  The OR gate implements the Boolean OR function where the output is logical 1 when just input is logical 1.  The standard symbol and the truth table for a two input OR gate is: NOT Gate  The NOT gate implements the Boolean NOT function where the output is the inverse of the input.  The standard symbol and the truth table for the NOT gate is: NOR Gate  The NOR is a combination of an OR followed by a NOT gate. The output is logical 1 when non of the inputs are logical 0  The standard symbol and the truth table for the NOR gate is: UNIVERSAL GATES  A universal gate is actually NAND and NOR gate. It is simply because they can be used to construct other gates. To build big and complex digital system, we only use NAND and NOR gate. NAND GATE AS UNIVERSAL GATE  NAND gate is used to make OR gate , NOT gate. These gate help us in making al the gates for eg: NAND gate as NOR gate: TTL CHARACTERISTICS Transistor-transistor logic (TTL)  based on bipolar transistors  one of the most widely used families for small- and medium-scale devices – rarely used for VLSI  typically operated from 5V supply  typical noise immunity about 1 – 1.6 V  many forms, some optimised for speed, power, etc.  high speed versions comparable to CMOS (~ 1.5 ns)  low-power versions down to about 1 mW/gate Introduction to CMOS logic family  CMOS stands for Complementary Metal Oxide Semiconductor. A complementary pair uses both p or n channel MOSFETs. CMOS CHARACTERISTICS Complementary metal oxide semiconductor (CMOS)  most widely used family for large-scale devices  combines high speed with low power consumption  usually operates from a single supply of 5 – 15 V  excellent noise immunity of about 30% of supply voltage  can be connected to a large number of gates (about 50)  many forms – some with tPD down to 1 ns  power consumption depends on speed (perhaps 1 mW Postulates OF Boolean Algebra  A statement that is not proved but assumed to be true is called the postulates .  The basic postulates of Boolean Algebra are:  Commutative laws  Associative laws  Distributed laws  Identity rule  Complement rule DEMORGAN’S THEOREMS  A great mathematician named demorgan gives two theorems of Boolean Algebra . These theorem are very useful and powerful identities used in Boolean Algebra. DeMorgan’s Theorem #1 A B A • B A • B A B A + B 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 A · B = A + B EQUAL KARNAUGH MAPS ( K-MAPS )  K-Map – A tool for representing Boolean function up to six variables .  K-Map are tables of row and columns with entries represent 1’s or 0’s of SOP and POS representation . 3. Groups must contain 1, 2, 4, 8, or in general 2' cells. That is if n = 1, a group will contain two 1's since 2' = 2. If n = 2, a group will contain four 1's since 2° = 4. jx—|_Group of 2 7 * '=+—Group of 4 0 i po 1] 9 a RIGHT \“ Sane 0 ian arin P| etuet Li RIGHT \/ SF 0 or tt 10 offi [it [1 ip—Sroup of 5 ie ee io] @] @] 2 WRONG > SF wo ot 10 of (TT YT 1 1 T¢—_Group of 5 Tailed maalaa se Dee ecdlneeel eet |e  00 Ol 11 10 Out= CD + CD+ ABC 1 1 1 ia i i 1 ‘| | 1 1 Out= CD + CD+ ABD Combinational Arithmetic Circuits  Addition:  Half Adder (HA).  Full Adder (FA).  Subtraction:  Half Subtractor.  Full Subtractor.  4 bit adder/subtracter  Adder and Subtractor IC (7484) HALF ADDER Adding two single-bit binary values, X, Y produces a sum S bit and a carry out C-out bit. This operation is called half addition and the circuit to realize it is called a half adder. X 0 0 1 1 Y 0 1 0 1 S 0 1 1 0 C-out 0 0 0 1 Half Adder Truth Table Inputs Outputs S(X,Y) = S (1,2) S = X’Y + XY’ S = X  Y C-out(x, y, C-in) = S (3) C-out = XY X Y Sum S C-out Half Adder X Y S C-OUT Full Adder Circuit Using XOR Full Adder X Y S C-inC-out XY YC-in C-outXC-in X X Y C-in Y C-in Sum S X Y C-in HALF SUBTRACTOR  Subtracting a single-bit binary value Y from anther X (I.e. X -Y ) produces a difference bit D and a borrow out bit B-out.  This operation is called half subtraction and the circuit to realize it is called a half subtractor. Half Subtractor • . X 0 0 1 1 Y 0 1 0 1 D 0 1 1 0 B-out 0 1 0 0 Half Subtractor Truth Table Inputs Outputs D(X,Y) = S (1,2) D = X’Y + XY’ D = X  Y B-out(x, y, C-in) = S (1) B-out = X’Y Half Subtractor X Y D B-OUT X Y Difference D B-out Full Subtractor Circuit Using XOR Difference D X Y B-in X’Y YB-in B-outX’B-in X’ X’ Y B-in Y B-in Full Subtractor X Y D B-inB-out PARALLEL BINARY ADDER  These adders are constructed by connecting two or more full adders.  A single full adder is used for adding two one-bit binary numbers and an input carry.  For the addition of binary numbers having more than one bit, additional full adders must be used. Block diagram of 4- bit binary Parallel Adder What is a Multiplexer (MUX)?  A MUX is a digital switch that has multiple inputs (sources) and a single output (destination).  The select lines determine which input is connected to the output.  MUX Types → 2-to-1 (1 select line) → 4-to-1 (2 select lines) → 8-to-1 (3 select lines) → 16-to-1 (4 select lines) 95 Multiplexer Block Diagram Select Lines Inputs (sources) Output (destination) 12N N M U X 4-to-1 Multiplexer (MUX) 96 B A Y 0 0 D0 0 1 D1 1 0 D2 1 1 D3 M U X D0 D1 D2 D3 Y B A 97 Multiplexers Z = A′.B'.C'.I0 + A'.B'.C.I1 + A'.B.C'.I2 + A'.B.C.I3 + A.B'.C'.I0 + A.B'.C.I1 + A'.B.C'.I2 + A.B.C.I3 MSB LSB A B C F 0 0 0 I0 0 0 1 I1 0 1 0 I2 0 1 1 I3 1 0 0 I4 1 0 1 I5 1 1 0 I6 1 1 1 I7