# Electronics. Digital Electronics

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1 Electronics Digital Electronics

2 Introduction Unlike a linear, or analogue circuit which contains signals that are constantly changing from one value to another, such as amplitude or frequency, digital circuits process signals that contain just two voltage levels or states, labelled logic "0" and logic "1". The voltages used to represent a digital circuit are called "logic levels". Generally, a logic "1" represents a higher voltage, which is referred to as a HIGH and a logic "0" is referred to as a LOW

3 Analogue Circuits Electronic circuits can be divided into two main categories. Analogue Circuits - Analogue or Linear circuits amplify or respond to continuously varying voltage levels over a period of time. The output from the potentiometer varies as the wiper terminal is rotated producing an infinite number of voltage points between 0 volts and V max. As the voltage output varies either slowly or rapidly there is no sudden change between two voltage levels giving a continuous output voltage. Examples of analogue signals include temperature, pressure, liquid levels and light intensity

4 Digital Circuits Digital Circuits - Digital circuits produce or respond too two distinct voltage levels representing either a Logic level "1" or a Logic level "0". As the wheel rotates, the optoswitch will generate an output that changes quickly beetween two discrete voltage levels. For example, 5V volts to 0 volt but NOT 2.5V, 3.1V or 4.6V. Then the major difference between an analogue signal or quantity and a digital quantity is that an "Analogue" quantity is continuously changing over time while a "Digital" quantity has discrete (step by step) values. LOW to HIGH or HIGH to LOW

5 Voltage Levels In all electronic circuits, only two logic levels are allowed and these levels are referred to as "logic 1 or logic 0", "high or low", "true or false". Most logic systems use positive logic, in which a logic "0" is represented by zero volts and a logic "1" is represented by a higher voltage, such as +5 volts. In standard TTL (transistor-transistor-logic) IC's there is a defined range of input and output voltage limits for defining what is a logic "1" value and what is a logic "0" value.

6 Noise Noise is the name given to a random and unwanted voltage that is induced into electronic circuits by external interference, such as from nearby switches, power supply fluctuations or from wires and other conductors that pick-up stray electromagnetic radiation. However, between these defined HIGH and LOW values lies what is generally called a "no-man's land" (the blue area's above) and if we apply a signal voltage of a value within this no-man's land area we do not know whether the logic gate will respond to it as a level "0" or as a level "1", and the output will become unpredictable.

7 Decimal to Binary Conversion The Decimal or "denary" counting system uses the Base of 10 numbering system where each digit in a number takes on one of ten possible values from 0 to 9, eg 213 (Two Hundred and Thirteen). In a decimal system each digit has a value ten times greater than its previous number and this decimal numbering system. In the decimal or denary system, the columns have values of units, tens, hundreds etc as we move from right to left and mathematically these values are written as 10 0, 10 1, 10 2, 10 3 etc (6 103) + (1 102) + (6 101) + (3 100) = 6163

8 Decimal to Binary Conversion Unlike the decimal numbering system which uses the base of 10, digital logic uses just two values or states, a logic level "1" or a logic level "0", so each "0" and "1" is considered to be a single digit in a Base of 2 orbinary numbering system. In the binary numbering system, each digit has a value twice that of the previous digit but can only have a value of either "1" or " Decimal Digit Value Binary Digit Value Then, the binary array of digits is equivalent to in decimal or denary.

9 Decimal to Binary Conversion Another method of converting Decimal to Binary number equivalents is to write down the decimal number and to continually divide by 2 (two) to give a result and a remainder of either a "1" or a "0" until the final result equals zero. Convert 83 to binary 83:2=41 remainder 1 LSB 41:2=20 remainder 1 20:2=10 remainder 0 10:2=5 remainder 0 5:2=2 reaminder 1 2:2=1 remainder 0 1:2=0 remainder 1 MSB =

10 Binary Numbers Binary numbers can be added together and subtracted just like decimal numbers with the result being combined into one of several size ranges depending upon the number of bits being used. The classification of individual bits into larger groups are generally referred to by the following more common names Number of Binary Digits (bits) Common Name 1 Bit 4 Nibble 8 Byte 16 Word 32 Double Word 64 Quad Word

11 Binary Numbers As micro-controller or microprocessor systems become increasingly larger, the individual binary digits (bits) are now grouped together into 8 s to form a single BYTE with most computer hardware such as hard drives and memory modules commonly indicate their size in Megabytes or even Gigabytes. Number of Bytes Common Name 1,024 (2 10 ) kilobyte (kb) 1,048,576 (2 20 ) Megabyte (Mb) 1,073,741,824 (2 30 ) Gigabyte (Gb) a very long number! (2 40 ) Terabyte (Tb)

12 Binary based other number systems The one main disadvantage of Binary Numbers is that the binary equivalent of a large decimal number can be quite long, which makes it difficult to both read or write without producing errors especially when working with 16 or 32-bit numbers. One common way of overcoming this problem is to arrange the binary numbers into groups Base, b Byte (8-bits) Word (16-bits) Decimal 0 to to 65, Binary to to Hexadecimal 00 to FF to FFFF 16 Octal 000 to to the memory of a computer would use hexadecimal numbers while the keyboard uses decimal numbers

13 Hexadecimal (16) the Hexadecimal numbering system uses only four digits to express a single 16-bit word length, and as a result it is the most commonly used Binary Numbering System for electronic and micro-electronic system Decimal 4-bit Binary Hexadecimal Decimal 4-bit Binary Hexadecimal A B C D E F (1+0) (1+1) Continuing upwards in groups of four

14 Counting: Using Hexadecimal Numbers 0...to...9, A,B,C,D,E,F, 10...to...19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21 Writing in binary form: 20F 16 =( ) 2 Conversions 3A 16 = ( ) 2 =0*128+0*64+1*32+1*16+1*8+0*4+1*2+0*1=58 3A 16 =3*16+10*1=58 20F 16 =2*256+0*16+15=527

15 Boolean (or Switching) Algebra Besides basic arithemtical operations, the binary numbers, which are inherently represents true or false logic states, are also used in logical operations. Boolean (or Switching) Algebra deals mainly with the theory that both logic and set operations are either "TRUE" or "FALSE" but not both at the same time. For example, A + A = A and not 2A as it would be in normal algebra. Boolean algebra is a simple and effective way of representing the switching action of standard Logic Gates and the basic logic statements.

16 The logic AND Function The Logic AND Function function states that two or more events must occur together and at the same time for an output action to occur. But the order at which they occur is unimportant as it does not affect the final result

17 The logic AND Function Switch A Switch B Output Description A and B are both open, lamp OFF A is open and B is closed, lamp OFF A is closed and B is open, lamp OFF A is closed and B is closed, lamp ON Boolean Expression (A AND B) A. B

18 TTL Logic Circuit The logic AND Gate TTL Logic Types 74LS08 Quad 2-input 74LS11 Triple 3-input 74LS21 Dual 4-input CMOS Logic Types CD4081 Quad 2-input CD4073 Triple 3-input CD4082 Dual 4-input

19 The Logic OR Function The Logic OR Function function states that an output action will occur or become TRUE if either one "OR" more events are TRUE, but the order at which they occur is unimportant as it does not affect the final result.

20 The Logic OR Function Switch A Switch B Output Description A is open and B is open, lamp OFF A is open and B is closed, lamp ON A is closed and B is open, lamp ON A is closed and B is closed, lamp ON Boolean Expression (A OR B) A + B

21 TTL Logic Circuit The logic OR Gate TTL Logic Types 74LS32 Quad 2-input CMOS Logic Types CD4071 Quad 2-input CD4075 Triple 3-input CD4072 Dual 4-input

22 The Logic XOR Function The Logic XOR Function function states that an output action will occur or become TRUE if and only if one "OR" event is TRUE. It excludes the state in which both OR events are true. XOR means "one or the other but not both". It represents the inequality function. The output is HIGH (1) if the inputs are not alike otherwise the output is LOW (0). Symbol Boolean Expression Q = A B Truth Table A B Q

23 The Logic NOT Function The Logic NOT Function is simply a single input inverter that changes the input of a logic level "1" to an output of logic level "0" and vice versa. They are more commonly known as Inverters because they invert the signal The logic NOT function is so called because its output state is NOT the same as its input state. It is generally denoted by a bar or overline ( ) over its input symbol which denotes the inversion operation.

24 The Logic NOT Function Switch 1 0 Boolean Expression Output 0 1 A

25 The NAND or Not AND function The NAND or Not AND function is a combination of the two separate logical functions, the AND function and the NOT function connected together in series. Switch A Switch B Output Description A and B are both open, lamp ON A is open and B is closed, lamp ON A is closed and B is open, lamp ON A is closed and B is closed, lamp OFF Boolean Expression (A AND B) A. B

26 The NAND or Not AND Gate TTL Logic Types 74LS00 Quad 2-input 74LS10 Triple 3-input 74LS20 Dual 4-input CMOS Logic Types CD4011 Quad 2-input CD4023 Triple 3-input CD4012 Dual 4-input

27 The Logic NOR Function the NOR or Not OR Gate is also a combination of two separate functions, theor function and the NOT function connected together in series. Switch A Switch B Output Description Both A and B are open, lamp ON A is open and B is closed, lamp OFF A is closed and B is open, lamp OFF A is closed and B is closed, lamp OFF Boolean Expression (A OR B) A + B

28 The NOR or Not OR Gate TTL Logic Types 74LS02 Quad 2-input 74LS27 Triple 3-input 74LS260 Dual 4-input CMOS Logic Types CD4001 Quad 2-input CD4025 Triple 3-input CD4002 Dual 4-input

29 The Laws of Boolean Boolean Algebra is the mathematics we use to analyse digital gates and circuits. We can use these "Laws of Boolean" to both reduce and simplify a complex Boolean expression in an attempt to reduce the number of logic gates required. The basic Laws of Boolean Algebra that relate to the Commutative Law allowing a change in position for addition and multiplication, the Associative Law allowing the removal of brackets for addition and multiplication, as well as the distributive Law allowing the factoring of an expression, are the same as in ordinary algebra.

30 The Laws of Boolean Annulment Law - A term AND ed with a "0" equals 0 or OR ed with a "1" will equal 1. A. 0 = 0, A variable AND'ed with 0 is always equal to 0. A + 1 = 1, A variable OR'ed with 1 is always equal to 1. Identity Law - A term OR ed with a "0" or AND ed with a "1" will always equal that term. A + 0 = A, A variable OR'ed with 0 is always equal to the variable. A. 1 = A, A variable AND'ed with 1 is always equal to the variable. Indempotent Law - An input AND ed with itself or OR ed with itself is equal to that input. A + A = A, A variable OR'ed with itself is always equal to the variable. A. A = A, A variable AND'ed with itself is always equal to the variable.

31 The Laws of Boolean Complement Law - A term AND ed with its complement equals "0" and a term OR ed with its complement equals "1". A. A = 0, A variable AND'ed with its complement is always equal to 0. A + A = 1, A variable OR'ed with its complement is always equal to 1. Commutative Law - The order of application of two separate terms is not important. A. B = B. A, The order in which two variables are AND'ed makes no difference. A + B = B + A, The order in which two variables are OR'ed makes no difference. Double Negation Law - A term that is inverted twice is equal to the original term. A = A, A double complement of a variable is always equal to the variable.

32 The Laws of Boolean de Morgan s Theorem - There are two "de Morgan s" rules or theorems, (1) Two separate terms NOR ed together is the same as the two terms inverted (Complement) andand ed for example, A+B = A. B (2) Two separate terms NAND ed together is the same as the two terms inverted (Complement) and OR ed for example, A.B = A +B.

33 The Laws of Boolean A B

34 The Boolean Algebra Example Using the above laws, simplify the following expression: Q=(A + B)(A + C) Q=(A + B)(A + C) Q=AA + AC + AB + BC - Distributive law Q=A + AC + AB + BC - Identity AND law (A.A = A) Q=A(1 + C) + AB + BC - Distributive law Q=A.1 + AB + BC - Identity OR law (1 + C = 1) Q=A(1 + B) + BC - Distributive law Q=A.1 + BC - Identity OR law (1 + B = 1) Q=A + BC - Identity AND law (A.1 = A) Then the expression: (A + B)(A + C) can be simplified to A + BC

35 The Boolean Algebra Find the Boolean algebra expression for the following system. AND NOT OR

36 The Boolean Algebra Inputs Intermediates Output C B A A.B.C B C B+C A.(B+C) Q

37 Pull up and Pull down resistors any "unused" inputs to the gates must be connected directly to either a logic level "1" or a logic level "0" by means of a suitable "Pull-up" or "Pull-down" resistor ( for example 1kΩ resistor ) to produce a fixed logic signal. This will prevent the unused input to the gate from "floating" about and producing false switching of the gate and circuit.

38 Combinational Logic Circuits Combinational Logic Circuits consist of inputs, two or more basic logic gates and outputs. The logic gates are combined in such a way that the output state depends entirely on the input states. Combinational logic circuits have "no memory", "timing" or "feedback loops", there operation is instantaneous. A combinational logic circuit performs an operation assigned logically by a Boolean expression or truth table.

39 Combinational Logic Circuits

40 The Multiplexer A data selector, more commonly called a Multiplexer, shortened to "Mux" or "MPX", are combinational logic switching devices that operate like a very fast acting multiple position rotary switch They connect or control, multiple input lines called "channels" consisting of either 2, 4, 8 or 16 individual inputs, one at a time to an output. The job of a multiplexer is to allow multiple signals to share a single common output.

41 The 4x1 Multiplexer Addressing b a Input Selected 0 0 A 0 1 B 1 0 C 1 1 D

42 The Demultiplexer The data distributor, known more commonly as a Demultiplexer or "Demux", takes one single input data line and then switches it to any one of a number of individual output lines one at a time. The demultiplexer converts a serial data signal at the input to a parallel data at its output lines as shown below. The function of the Demultiplexer is to switch one common data input line to any one of the 4 output data lines A to D in our example above

43 The 1x4 Multiplexer Addressing b a Output Selected 0 0 A 0 1 B 1 0 C 1 1 D

44 Binary Encoder Binary Encoder takes ALL its data inputs one at a time and then converts them into a single encoded output. So we can say that a binary encoder, is a multi-input combinational logic circuit that converts the logic level "1" data at its inputs into an equivalent binary code at its output. Generally, digital encoders produce outputs of 2-bit, 3-bit or 4-bit codes depending upon the number of data input lines. (e.g. Keyboard)

45 The binary encoder Compass Binary Output Direction Q 0 Q 1 Q 2 North North-East East South-East South South-West West North-West 1 1 1

46 The Decoder Encoder is basically, a combinational type logic circuit that converts the binary code data at its input into one of a number of different output lines, one at a time producing an equivalent decimal code at its output. A decoders output code normally has more bits than its input code and practical binary decoder circuits include, 2-to-4, 3-to-8 and 4-to-16 line configurations.

47 BCD to 7-Segment Display Decoder Decoder IC, is a device which converts one digital format into another and the most commonly used device for doing this is the Binary Coded Decimal (BCD) to 7-Segment Display Decoder. A standard 7-segment LED display generally has 8 input connections, one for each LED segment and one that acts as a common terminal or connection for all the internal segments. Some single displays have an additional input pin for the decimal point in their lower right or left hand corner.

48 BCD to 7-Segment Display Decoder Individual Segments a b c d e f g Display Individual Segments a b c d e f g Display 8 9 A b C d E F

49 Binary Coded Decimal (BCD) numbers are made up using just 4 data bits similar to the Hexadecimal numbers but unlike hexadecimal numbers that range in full from 0 through to F, BCD numbers only range from 0 to 9, with the binary number patterns of 1010 through to 1111 (A to F) being invalid inputs for this type of display and so are not used BCD Numbers Decimal Binary Pattern BCD N.A.

50 BCD to 7-Segment Display Decoder

51 Binary Adder The Binary Adder is made up from standard AND and Ex-OR gates and allow us to "add" together single bit binary numbers, a and b to produce two outputs, the SUM of the addition and a CARRY called the Carry-out, ( C out ) bit Symbol Boolean Expression: Sum = A B Truth Table A B SUM CARRY Carry = A. B

52 Binary Comparator Digital or Binary Comparators are made up from standard AND, NOR and NOT gates that compare the digital signals present at their input terminals and produce an output depending upon the condition of those inputs. Inputs Outputs B A A > B A = B A < B

53 Sequential Logic Sequential Logic circuits have some form of inherent "Memory" built in to them as they are able to take into account their previous input state as well as those actually present, a sort of "before" and "after" is involved with sequential circuits. The output state of a sequential logic circuit is a function of the following three states, the "present input", the "past input" and/or the "past output". Sequential Logic circuits remember these conditions and stay fixed in their current state until the next clock signal changes one of the states, giving sequential logic circuits "Memory". Sequential logic circuits are generally termed as two state or Bistable devices which can have their output or outputs set in one of two basic states, a logic level "1" or a logic level "0" and will remain "latched" indefinitely in this current state or condition until some other input trigger pulse or signal is applied which will cause the bistable to change its state once again.

54 Sequential Logic Representation The word "Sequential" means that things happen in a "sequence", one after another and in Sequential Logic circuits, the actual clock signal determines when things will happen next. 1. Event Driven - asynchronous circuits that change state immediately when enabled. 2. Clock Driven - synchronous circuits that are synchronised to a specific clock signal. 3. Pulse Driven - which is a combination of the two that responds to triggering pulses.

55 RS Flip Flop The SR flip-flop, also known as a SR Latch, can be considered as one of the most basic sequential logic circuit possible. This simple flip-flop is basically a one-bit memory bistable device that has two inputs, one which will "SET" the device (meaning the output = "1"), and is labelled S and another which will "RESET" the device (meaning the output = "0"), labelled R. Then the SR description stands for "Set-Reset". The reset input resets the flip-flop back to its original state with an output Q that will be either at a logic level "1" or logic "0" depending upon this set/reset condition

56 RS Flip Flop Active low RS Flip flop implementation with NAND gates State S R Q Q Description Set Set Q» no change Reset Reset Q» no change Invalid memory with Q = memory with Q = 1

57 Nor gate RS Flip Flop SR Flip Flop

58 JK Flip Flop The JK flip-flop is basically a gated SR flip-flop with the addition of a clock input circuitry that prevents the illegal or invalid output condition that can occur when both inputs S and R are equal to logic level "1". Due to this additional clocked input, a JK flip-flop has four possible input combinations, "logic 1", "logic 0", "no change" and "toggle"

59 JK Flip Flop Truth Table C J K Q(n) Q(n+1) Delete ,1 0,0 Write ,0 1,1 Save ,1 0,1 Toggle ,0 0,1

60 D Flip Flop The D flip-flop is by far the most important of the clocked flip-flops as it ensures that ensures that inputs S and R are never equal to one at the same time. D-type flip-flops are constructed from a gated SR flip-flopwith an inverter added between the S and the R inputs to allow for a single D (data) input. This single data input D is used in place of the "set" signal, and the inverter is used to generate the complementary "reset" input thereby making a level-sensitive D-type flip-flop from a level-sensitive RSlatch as now S = D and R = not D

61 D Flip Flop Clk D Q Q Description» 0 X Q Q Memory no change» Reset Q» 0» Set Q» 1

62 D Flip Flop / Data Latch

63 D Flip Flop- Frequency divider

64 The Clock As seen in previous applications, Sequential Logic circuits to operate in a "sequential" way, they require the addition of a clock pulse or timing signal to cause them to change their state. Clock pulses are generally continuous square or rectangular shaped waveform that is produced by a pulse generator. This multivibrator circuit oscillates between a "HIGH" state and a "LOW" state producing a continuous output. Sequential logic circuits that use the clock signal for synchronization are dependant upon the frequency and and clock pulse width to activate there switching action.

65 The Clock Active HIGH - if the state changes occur at the clock's rising edge or during the clock width. Active LOW - if the state changes occur at the clock's falling edge. Duty Cycle - is the ratio of clock width and clock period. Clock Width - this is the time during which the value of the clock signal is equal to one. Clock Period - this is the time between successive transitions in the same direction, i.e., between two rising or two falling edges. Clock Frequency - the clock frequency is the reciprocal of the clock period, frequency = 1/clock period

66 The Clock There are basically three types of clock pulse generation circuits: Astable - A free-running multivibrator that has NO stable states but switches continuously between two states this action produces a train of square wave pulses at a fixed frequency. Monostable - A one-shot multivibrator that has only ONE stable state and is triggered externally with it returning back to its first stable state. Bistable - A flip-flop that has TWO stable states that produces a single pulse either positive or negative in value.

67 NE555 Astable Multivibrator Astable Multivibrators are a type of free running oscillator that have no permanent "meta" or "steady" state but are continually changing there output from one state ("LOW") to the other state ("HIGH") The continual switching action from "HIGH" to "LOW" and "LOW" to "HIGH" produces a continuous and stable square wave output that switches abruptly between the two logic levels making it ideal for timing and clock pulse applications. t 1 = (R1 + R2) C1 t 2 = (R2) C1 T = t 1 + t 2

68 NAND Gate Monostable Circuit Monostable Multivibrators or "one-shot" pulse generators are used to convert short sharp pulses into wider ones for timing applications. Monostable multivibrators generate a single output pulse, either "high" or "low", when a suitable external trigger signal or pulse T is applied.

69 The bistable multivibrator The bistable multivibrator can be switched over from one stable state to the other by the application of an external trigger pulse thus, it requires two external trigger pulses before it returns back to its original state

70 Thanks for your interest.

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