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Important Terms - Number Systems And Conversion

Published in: Mathematics
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    Rujuta M

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It contains all the basic necessary information about number systems and conversion, logic gates, flip flops and basic electronics concepts like resistor, capacitor, MOSFET and transistor.

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    Important terms Number System
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    Number System ' Decimal number system(base 10) : 9 0000 00 Binary number system(base 2): O,l(bits) ' Hexadecimal number system(base 16) :
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    Decirnal o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Binary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 Hex o 1 2 3 4 5 6 7 8 9 c
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    Conversion from decimal to binary and binary to decimal Ex. Convert 2510 to binary 25/2 12/2 6/2 3/2 1/2 Quotient 12 6 3 1 Remainder LSB (least significant bit) 1 1 1 MSB (most significant bit) Therefore 25 = 110012 Ex. Convert 110012 to decimal Weight: Digits: Sum: 24 1 16 + 23 1 22 O 21 O 20 1 1 = 2510
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    Conversion from binary to hex and hex to binary 1001 9 F Ex. Convert hex 29B to binary 2 9 0010 1001 0101 5 B 1011
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    Conversion from decimal to hex Ex. Convert 4510 to hex 32 16 8 4 2 1 4510 = 0010 11012 - 2D 16 Ex. Convert 62910 to hex 512 256 128 64 1 1 1 32 + 8 4 + 1 32 16 8 4 2 1 1 10101 = 45 16 62910 = 512+64+32+16+4+1 = 0010 0111 01012 — 275 Convert to binary first and then convert to hex Convert directly from decimal to hex by repeated division, keeping track of the remainders
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    Converting hex to decimal Ex. 6B2 16 = 0110 1011 00102 1024 512 256 128 64 32 16 8 4 2 1 1 1 o 1 o 1 10010 1024 + 512 + 128 + 32 + 16 +2 = 171410 Convert from hex to binary and then to decimal Convert directly from hex to decimal by summing the weight of all digits
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    Addition and Subtraction of hex numbers Ex. Perform hex addition: 23D9 + 94BE 23 - 16 = 23D9 LSD: 9+ 14 = 23 25 16 7 w/ carry 16 = 9 w/ carry 8897 1+ 13 + 11 = 25 1+3+4=8 MSD: 2+9 = B Ex. Perform hex subtraction: 59F — 2B8 59F I-. 2B8 2E7 LSD: 15-8=7 9 + 16 — Il 5-1-2=2 = 14 = E
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    ASCII code:American Standard Code for Information Interchanqe The ASCII (pronounced "ask-E") code assigns binary patterns for Numbers 0 to 9 All the letters of English alphabet, uppercase and lowercase Many control codes and punctuation marks
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    The ASCII system uses 7 bits to represent each code Hex Selected ASCII codes 42 43 44 59 Symbol Hex 62 63 64 79 Symbol
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    ASCII code and BCD for digits 0 - 9 1 Key ASCII (hex) 30 31 32 33 34 35 36 37 38 39 Binary 011 0000 011 0001 011 0010 011 0011 011 0100 011 0101 011 0110 011 0111 011 1000 011 1001 BCD (unpacked) 0000 0000 0000 0001 0000 0010 0000 0011 0000 0100 0000 0101 0000 0110 0000 0111 0000 1000 0000 1001
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    Packed BCD to ASCII and ASCII to Packed BCD conversion Packed BCD 29H 0010 1001 key ASCII 4 7 Unpacked BCD 02H & 09H 0000 0010 & 0000 1001 Unpacked BCD ASCII 32H & 39H 0011 0010 & 0011 1001 Packed BCD 0100 0111 or 47H
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    5 4 3 2 1 C) Binary Logic Logic I Logic 0 Two voltage levels can be represented as the two digits 0 and 1 Signals in digital electronics have two distinct voltage levels with built-in tolerances for variations in the voltage A valid digital signal should be within either of the two shaded areas
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    Important terms Basic Digital concepts
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    AND gate Boolean Expression Logic gates Logic Diagram Symbol Computer Science Illuminated, Dale and Lewis OR gate Boolean Expression x Logic Diagram Symbol Truth Table Truth Table Computer Scence Illuminated, Dale and Lewcs
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    Tri-state buffer Inverter Boolean Expression Computer Science Illuminated, Dale and Lewis Logic Diagram Symbol XOR gate Boolean Expression X Logic Diagram Symbol Truth Table Truth Table Computer Science Illuminated, Dale and Lewis
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    Tri state buffer tri —state buffer •writh tri —state buffer writh active lowr control active high control c 1 z z x c 1 z x z A tri-state buffer has two inputs: a data input x and a control input c. The control input acts like a valve. When the control input is active, the output is the input. That is, it behaves just like a normal buffer. The "valve" is open.
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    NAND gate Boolean Expression Logic Diagram Symbol Computer Science Illuminated, Dale and Lewis NOR gate Boolean Expression Logic Diagram Symbol Truth Table Truth Table
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    Decoders Decoders are widely used for address decoding in computer design Address Decoders LSB Address decoder for 9 (10012) The output will be I if and only if the input is 1001 2 LSB Address decoder for 5 (01012) The output will be I if and only if the input is 0101 2
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    Flip-flops or Latch Flip-flops are frequently used to store data o x 1 0 Next state of Q No change Q 0; Reset state Q l; Set state )igital Design, Mano (a) Logic diagram (b) Function table
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    The unit of data size Bit: a binary digit that can have the value Byte: 8 bits Nibble: half of a bye, or 4 bits Word: two bytes, or 16 bits The terms used to describe amounts of memory in IBM PCs and compatibles Kilobyte (K): 210 bytes Megabyte (M) : 220 bytes, over 1 million Gigabyte (G) : 230 bytes, over 1 billion Terabyte (T) : 240 bytes, over 1 trillion
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    The CPU is connected to memory and I/O through strips of wire called a bus Carries information from place to place Address bus • Data bus • Control bus Keyboard CPU Read/ Write Address bus Data bus Control bus
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    Inside CPUs Flags Program Counter Instruction Register ALU Instruction decoder, timing, and control Intemal Register A buses Register B Register C Register D
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    Important terms Basic Electronics concepts
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    Voltage Source Voltage Source t Positive Pressure Negative Pressure Pressure is analagous to Voltage Figure 1-3: 'Voltage in an electrical circuit is analogous to pressure in a fluid
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    Symbols AC supply AC or supply CPC supply S 'vvitch Output Load
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    Resistor Resistor Restricts Current Restriction of Current Flow Figure 1-4: Resistance in an electrical circuit is analogous to a restriction in the flow of a fluid
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    Zero Volts ground' Current (l) through Resistor (R) causes Voltage drop (V) V-IR t Power dissipated in Resistor €2 Positive Pressure Zero Reference Atmospheric Pressure Figure 1-5: Voltage across R is equal to current multiplied by resistance.
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    Two capacitors connected in parallel. Total charge =Q Potential difference = V eq ceq Cl+C2 The equivalent capacitance of two capacitors connected in parallel is the sum of the individual capacitances. ceq cz Two capacitors connected in series. The net result is that both capacitors possess the same stored charge Q The potential drops VI and V 2 across two capacitors is different. The sum of these drops equals the total potential drop applied across the input and output wires 1 ceq Q/v ceq 1 ceq V VI +14 1 1 The reciprocal of the equivalent capacitance of two capacitors connected in series is the sum of the reciprocals of the individual capacitances. l/ceq - EIN-I (l/cz).
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    Series and parallel capacitors For parallel capacitors, V is the same, so total charge is given by QI+Q2 ctv+qv Hence: q +Q For series capacitors, the CHARGE on each capacitor must be the same and equal to the net charge. [The centre electrode has a net charge of zero] TOT TOT Hence:
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    Inductors in Series and Parallel For inductors in series 1.2 LEQ = Ll + L2 For inductors in parallel LEQ
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    Summary of Capacitor and Inductor Formulae I-V relationship Stored energy Dissipated energy Series equivalent Parallel equivalent Current/voltage timing Capacitor dt w cv2 2 O 1 1 Cl+C2 Cuneent leads voltage Inductor v L dt L12 2 Ll+L2 1 1 Voltage leads cunent Resistor V IR Rl+R2 1 1 Cunent in phase with voltage
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    Diode Current Diode "On" Diode "Off" Current Flows No Current Flows Diode is analgous to a one-way valve. Current can only flow in one direction. Valve "Open" Valve "Closed" Figure 1-6: A diode to electricity is analogous to a valve in the flow of a fluid.
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    Base t Current Flow Control Collector Emitter "Sink" "Source" Current Flow Base Current Flow Collector Emitter "Source" Control "Sink" Current Flow Figure 1-8: Operation of a bipolar NPN transistor Sinking Sou rcing Figure 1-7: Operation of a bipolar PNP transistor, provides a path to supply common provides a path to supply source (+)
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    Transistor Inverter Input 1 -> Output O Resistor Sources Current Transistor ON (shorted) Transistor Switch "ON" Output Sinks Current Transistor Inverter Equivalent Circuit Transistor ON (shorted) Equivalent Circuit Output Sinks Current Figure 1-10: The transistor inverter; input = 7 and transistor ON. The transistor ON configuration is at left and the equivalent circuit is at right. Transistor Inverter Input 0 -> Output 1 Input Sinks Current Resistor Sources Current Transistor OFF (open) Transistor Inverter Equivalent Circuit Equivalent Circuit Resistor Sources Current Transistor OFF (open) Transistor Switch "OFF" Figure 1-17: 'The transistor inverter; input = 0 and transistor OFF. The transistor OFF configuration is at left and the equivalent circuit is at right.
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    MOSFET and Transistor N-channel s P-channel s Open-drain refers to the drain terminal of a MOS FET transistor. Open-collector is the same concept on a bipolar device.
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    Open drain and open collector Open-collector/open-drain devices ' sink (flow) current when low voltage active (logic O) state. High impedance (no current flows) When high voltage non-active (logic 1) state. These devices usually operate with an external pull-up resistor that holds the signal line high until a device on the wire sinks enough current to pull the line low. An open-collector/open-drain signal wire can also be bi-directional. Bi-directional means that a device can both output and input a signal on the wire at the same time Sinking provides o poth to supply common Sourcing provides a path to supply source (+)
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    Pull-up resistor Internal pull-up resistor External pull-up resistor Weak pull-up resistor(high value resistor for pulling signal to vcc) Vcc Inpu P Input without Pul up Resistor vcc 10k Input Pin Pullup Resistor Circuit Example
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    When the switch is open it will cause the input of the chip to float. ' Depending on the device this could lead to undefined operation of the input, ' oscillation between states, high power consumption or physical damage to the device, The answer is the pull up resistor.
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    ' Switch open —input pin voltage is VCC ' i.e less current and small voltage drop across resistor. Switch close-input pin voltage is nearly equal to ground .i.e current will flow through resistor through switch to ground. The input pin of the microcontroller will have either Vcc or ground. A typical value for a pull up resistor is usually betweeen 10k and 100k Q.
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    Bypass and Decoupling capacitors IOuF — O.1uF Fig 13. Bypass and decoupling capacitors Power Decoupling Bypassing Ground Plano, A capacitor allows ac voltage to pass through and blocks dc voltage. This has been used in many electronic applications.
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    Bypass capacitors A Bypass Capacitor offers a low impedance path to high frequency current flow, reducing the noise current on power supply lines. Usually, a 0.1 uF capacitor is used it should be as close to the device as possible. wc.c Circuit VOtS 5.05 5.04 5.03 5.02 5.01 5.00 4.98 No Bypass 4.97 L'V$th Bypass 4. SS 4.95 Time
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    decoupling capacitors A Decoupling Capacitor provides isolation of two circuits; this will prevent noise from being transmitted from one circuit to the other. ' It can be used with an inductor, forming a low pass filter. A 10 uF works well in these cases, and it should be connected close to the power supply.
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    Impedance Definition Impedance, represented by the symbol Z, is a measure of the opposition to electrical flow. It is measured in ohms. For DC systems, impedance and resistance are the same, defined as the voltage across an element divided by the current (R = V/l). In AC systems, the "reactance" enters the equation due to the frequency- dependent contributions of capacitance and inductance. Impedance in an AC system is still measured in ohms and represented by the equation Z = V/l, but V and I are frequency-dependent. Reactance, denoted X, is like an AC counterpart of DC (direct current) resistance. It is a form of opposition that electronic components because of capacitance or inductance.
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    Z=R+jX where Z is the impedance, measured in ohms. R is the resistance, measured in ohms. X is the reactance, measured in ohms. Both capacitive reactance and inductive reactance contribute to the total reactance 1 wc where - 2TfL 1 wc 1 2TfC 'XC is the capacitive reactance, measured in ohms •XL is the inductive reactance, measured in ohms Although XL and XC are both positive by convention, the capacitive reactance makes a negative contribution to total reactance. Hence, elf X > O the reactance is said to be inductive. then the impedance is purely resistive. , the reactance is said to be capacitive.
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    1 1 wc 2TfC Capacitive reactance is an opposition to the change of voltage across an element = - 2TfL Inductive reactance is an opposition to the change of current on an inductive element
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    High Level Assembly Machine Register Transfer Gate Circuit Sum Sum + 1 MOV BX,SUM INC (BX) Fetch Instruction, Increment PC, Load ALU with SUM Figure 2-1 "Layers" of a computer system

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