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  1. 1. The Logic "AND" GateDefinitionA Logic AND Gate is a type of digital logic gate that has an output which is normally at logiclevel "0" and only goes "HIGH" to a logic level "1" when ALL of its inputs are at logic level"1". The output of a Logic AND Gate only returns "LOW" again when ANY of its inputs are ata logic level "0". The logic or Boolean expression given for a logic AND gate is that for LogicalMultiplication which is denoted by a single dot or full stop symbol, ( . ) giving us the Booleanexpression of: A.B = Q.Then we can define the operation of a 2-input logic AND gate as being: "If both A and B are true, then Q is true"The Digital Logic "AND" Gate2-input AND Gate Symbol Truth Table B A Q 0 0 0 0 1 0 2-input AND Gate 1 0 0 1 1 1 Boolean Expression Q = A.B Read as A AND B gives Q3-input AND Gate Symbol Truth Table C B A Q 0 0 0 0 0 0 1 0 0 1 0 0 3-input AND Gate 0 1 1 0 1 0 0 0
  2. 2. 1 0 1 0 1 1 0 0 1 1 1 1 Boolean Expression Q = A.B.C Read as A AND B AND C gives QBecause the Boolean expression for the logic AND function is defined as (.), which is a binaryoperation, AND gates can be cascaded together to form any number of individual inputs.However, commercial available AND gate ICs are only available in standard 2, 3, or 4-inputpackages. If additional inputs are required, then standard AND gates will need to be cascadedtogether to obtain the required input value, for example.Multi-input AND GateThe Boolean Expression for this 6-input AND gate will therefore be: Q = (A.B).(C.D).(E.F)The Logic "OR" GateDefinitionA Logic OR Gate or Inclusive-OR gate is a type of digital logic gate that has an output which isnormally at logic level "0" and only goes "HIGH" to a logic level "1" when one or more of itsinputs are at logic level "1". The output, Q of a Logic OR Gate only returns "LOW" again whenALL of its inputs are at a logic level "0". The logic or Boolean expression given for a logic ORgate is that for Logical Addition which is denoted by a plus sign, ( + ) giving us the Booleanexpression of: A+B = Q.Then we can define the operation of a 2-input logic OR gate as being:
  3. 3. "If either A or B is true, then Q is true"The Digital Logic "OR" Gate2-input OR Gate Symbol Truth Table B A Q 0 0 0 0 1 1 2-input OR Gate 1 0 1 1 1 1 Boolean Expression Q = A+B Read as A OR B gives Q3-input OR Gate Symbol Truth Table C B A Q 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 3-input OR Gate 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 Boolean Expression Q = A+B+C Read as A OR B OR C gives QLike the AND gate, the OR function can have any number of individual inputs. However,commercial available OR gates are available in 2, 3, or 4 inputs types. Additional inputs willrequire gates to be cascaded together for example.Multi-input OR Gate
  4. 4. The Boolean Expression for this 6-input OR gate will therefore be: Q = (A+B)+(C+D)+(E+F)The Digital Logic "NOT" GateDefinitionThe digital Logic NOT Gate is the most basic of all the logical gates and is sometimes referredto as an Inverting Buffer or simply a Digital Inverter. It is a single input device which has anoutput level that is normally at logic level "1" and goes "LOW" to a logic level "0" when itssingle input is at logic level "1", in other words it "inverts" (complements) its input signal. Theoutput from a NOT gate only returns "HIGH" again when its input is at logic level "0" giving usthe Boolean expression of: A = Q.Then we can define the operation of a single input logic NOT gate as being: "If A is NOT true, then Q is true"The Digital Inverter or NOT gate Symbol Truth Table A Q 0 1 Inverter or NOT Gate 1 0 Boolean Expression Q = not A or A Read as inverse of A gives Q
  5. 5. Logic NOT gates provide the complement of their input signal and are so called because whentheir input signal is "HIGH" their output state will NOT be "HIGH". Likewise, when their inputsignal is "LOW" their output state will NOT be "LOW". As they are single input devices, logicNOT gates are not normally classed as "decision" making devices or even as a gate, such as theAND or OR gates which have two or more logic inputs. Commercial available NOT gates ICsare available in either 4 or 6 individual gates within a single i.c. package.The Logic "NAND" GateDefinitionThe Logic NAND Gate is a combination of the digital logic AND gate with that of an inverter orNOT gate connected together in series. The NAND (Not - AND) gate has an output that isnormally at logic level "1" and only goes "LOW" to logic level "0" when ALL of its inputs are atlogic level "1". The Logic NAND Gate is the reverse or "Complementary" form of the ANDgate we have seen previously.Logic NAND Gate EquivalenceThe logic or Boolean expression given for a logic NAND gate is that for Logical Addition, whichis the opposite to the AND gate, and which it performs on the complements of the inputs. TheBoolean expression for a logic NAND gate is denoted by a single dot or full stop symbol, ( . )with a line or Overline, ( ‾‾ ) over the expression to signify the NOT or logical negation of theNAND gate giving us the Boolean expression of: A.B = Q.The Digital Logic "NAND" Gate2-input NAND Gate Symbol Truth Table B A Q 0 0 1 0 1 1 2-input NAND Gate 1 0 1 1 1 0
  6. 6. Boolean Expression Q = A.B Read as A AND B gives NOT Q3-input NAND Gate Symbol Truth Table C B A Q 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 3-input NAND Gate 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 Boolean Expression Q = A.B.C Read as A AND B AND C gives NOT QAs with the AND function seen previously, the NAND function can also have any number ofindividual inputs and commercial available NAND Gate i.c.´s are available in standard 2, 3, or 4input typesThe Logic "NOR" GateDefinitionThe Logic NOR Gate or Inclusive-NOR gate is a combination of the digital logic OR gate withthat of an inverter or NOT gate connected together in series. The NOR (Not - OR) gate has anoutput that is normally at logic level "1" and only goes "LOW" to logic level "0" when ANY ofits inputs are at logic level "1". The Logic NOR Gate is the reverse or "Complementary" form ofthe OR gate we have seen previously.NOR Gate EquivalentThe logic or Boolean expression given for a logic NOR gate is that for Logical Multiplicationwhich it performs on the complements of the inputs. The Boolean expression for a logic NOR
  7. 7. gate is denoted by a plus sign, ( + ) with a line or Overline, ( ‾‾ ) over the expression to signifythe NOT or logical negation of the NOR gate giving us the Boolean expression of: A+B = Q.Then we can define the operation of a 2-input logic NOR gate as being: "If both A and B are NOT true, then Q is true"The Digital Logic "NOR" Gate2-input NOR Gate Symbol Truth Table B A Q 0 0 1 0 1 0 2-input NOR Gate 1 0 0 1 1 0 Boolean Expression Q = A+B Read as A OR B gives NOT Q3-input NOR Gate Symbol Truth Table C B A Q 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 3-input NOR Gate 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 Boolean Expression Q = A+B+C Read as A OR B OR C gives NOT QAs with the OR function, the NOR function can also have any number of individual inputs andcommercial available NOR Gate ICs are available in standard 2, 3, or 4 input types.
  8. 8. The Exclusive-OR GateDefinitionPreviously, we have seen that for a 2-input OR gate, if A = "1", OR B = "1", OR BOTH A + B= "1" then the output from the gate is also at logic level "1" and this is known as an Inclusive-ORfunction because it includes the case of Q = "1" when both A and B = "1". If however, an output"1" is obtained ONLY when A = "1" or when B = "1" but NOT both together at the same time,then this type of gate is known as an Exclusive-OR function or an Ex-Or function for shortbecause it excludes the "OR BOTH" case of Q = "1" when both A and B = "1".In other words the output of an Exclusive-OR gate ONLY goes "HIGH" when its two inputterminals are at "DIFFERENT" logic levels with respect to each other and they can both be atlogic level "1" or both at logic level "0" giving us the Boolean expressionof: Q = (A B) = A.B + A.BThe Exclusive-OR Gate function is achieved is achieved by combining standard gates togetherto form more complex gate functions. An example of a 2-input Exclusive-OR gate is givenbelow.The Digital Logic "Ex-OR" Gate2-input Ex-OR Gate Symbol Truth Table B A Q 0 0 0 0 1 1 2-input Ex-OR Gate 1 0 1 1 1 0 Boolean Expression Q = A B Read as A OR B but NOT BOTH gives QThen, the logic function implemented by a 2-input Ex-OR is given as "either A OR B but NOTboth" will give an output at Q. In general, an Ex-OR gate will give an output value of logic "1"ONLY when there are an ODD number of 1s on the inputs to the gate. Then an Ex-OR functionwith more than two inputs is called an "odd function" or modulo-2-sum (Mod-2-SUM), not anEx-OR. This description can be expanded to apply to any number of individual inputs as shownbelow for a 3-input Ex-OR gate.3-input Ex-OR Gate
  9. 9. Symbol Truth Table C B A Q 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 3-input Ex-OR Gate 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 Boolean Expression Q = A B C Read as "any ODD number of Inputs" gives QThe symbol used to denote an Exclusive-OR function is slightly different to that for the standardInclusive-OR gate. The logic or Boolean expression given for a logic OR gate is that of logicaladdition which is denoted by a standard plus sign. The symbol used to describe the Booleanexpression for an Exclusive-OR function is a plus sign, ( + ) within a circle, ( Ο ). Thisexclusive-OR symbol also represents the mathematical "direct sum of sub-objects" expression,with the resulting symbol for an Exclusive-OR function being given as: ( ).We said previously that the Ex-OR function is a combination of different basic logic gates andusing the 2-input truth table above, we can expand the Ex-OR function to:Q = (A B) = (A+B).(A.B) which means we can realise this new expression using thefollowing individual gates.SR Flip-FlopThe SR flip-flop, also known as a SR Latch, can be considered as one of the most basicsequential logic circuit possible. This simple flip-flop is basically a one-bit memory bistabledevice that has two inputs, one which will "SET" the device (meaning the output = "1"), and islabelled 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 itsoriginal state with an output Q that will be either at a logic level "1" or logic "0" depending uponthis set/reset condition.
  10. 10. A basic NAND gate SR flip-flop circuit provides feedback from both of its outputs back to itsopposing inputs and is commonly used in memory circuits to store a single data bit. Then the SRflip-flop actually has three inputs, Set, Reset and its current output Q relating to its current stateor history. The term "Flip-flop" relates to the actual operation of the device, as it can be "flipped"into one logic Set state or "flopped" back into the opposing logic Reset state.The NAND Gate SR Flip-FlopThe simplest way to make any basic single bit set-reset SR flip-flop is to connect together a pairof cross-coupled 2-input NAND gates as shown, to form a Set-Reset Bistable also known as anactive LOW SR NAND Gate Latch, so that there is feedback from each output to one of theother NAND gate inputs. This device consists of two inputs, one called the Set, S and the othercalled the Reset, R with two corresponding outputs Q and its inverse or complement Q (not-Q) asshown below.The Basic SR Flip-flopThe Set StateConsider the circuit shown above. If the input R is at logic level "0" (R = 0) and input S is atlogic level "1" (S = 1), the NAND gate Y has at least one of its inputs at logic "0" therefore, itsoutput Q must be at a logic level "1" (NAND Gate principles). Output Q is also fed back to input"A" and so both inputs to NAND gate X are at logic level "1", and therefore its output Q must beat logic level "0".Again NAND gate principals. If the reset input R changes state, and goes HIGH to logic "1" withS remaining HIGH also at logic level "1", NAND gate Y inputs are now R = "1" and B = "0".Since one of its inputs is still at logic level "0" the output at Q still remains HIGH at logic level"1" and there is no change of state. Therefore, the flip-flop circuit is said to be "Latched" or "Set"with Q = "1" and Q = "0".Reset StateIn this second stable state, Q is at logic level "0", (not Q = "0") its inverse output at Q is at logiclevel "1", (Q = "1"), and is given by R = "1" and S = "0". As gate X has one of its inputs at logic
  11. 11. "0" its output Q must equal logic level "1" (again NAND gate principles). Output Q is fed backto input "B", so both inputs to NAND gate Y are at logic "1", therefore, Q = "0".If the set input, S now changes state to logic "1" with input R remaining at logic "1", output Qstill remains LOW at logic level "0" and there is no change of state. Therefore, the flip-flopcircuits "Reset" state has also been latched and we can define this "set/reset" action in thefollowing truth table.Truth Table for this Set-Reset Function State S R Q Q Description 1 0 1 0 Set Q » 1 Set 1 1 1 0 no change 0 1 0 1 Reset Q » 0 Reset 1 1 0 1 no change 0 0 0 1 memory with Q = 0 Invalid 0 0 1 0 memory with Q = 1It can be seen that when both inputs S = "1" and R = "1" the outputs Q and Q can be at eitherlogic level "1" or "0", depending upon the state of inputs S or R BEFORE this input conditionexisted. However, input state R = "0" and S = "0" is an undesirable or invalid condition and mustbe avoided because this will give both outputs Q and Q to be at logic level "1" at the same timeand we would normally want Q to be the inverse of Q.However, if the two inputs are now switched "HIGH" again after this condition to logic "1", boththe outputs will go "LOW" resulting in the flip-flop becoming unstable and switch to anunknown data state based upon the unbalance. This unbalance can cause one of the outputs toswitch faster than the other resulting in the flip-flop switching to one state or the other whichmay not be the required state and data corruption will exist. This unstable condition is known asits Meta-stable state.Then, a bistable SR flip-flop or SR latch is activated or set by a logic "1" applied to its S inputand deactivated or reset by a logic "1" applied to its R. The SR flip-flop is said to be in an"invalid" condition (Meta-stable) if both the set and reset inputs are activated simultaneously.The D flip-flopOne of the main disadvantages of the basic SR NAND Gate bistable circuit is that theindeterminate input condition of "SET" = logic "0" and "RESET" = logic "0" is forbidden. Thisstate will force both outputs to be at logic "1", over-riding the feedback latching action andwhichever input goes to logic level "1" first will lose control, while the other input still at logic"0" controls the resulting state of the latch.
  12. 12. But in order to prevent this from happening an inverter can be connected between the "SET" andthe "RESET" inputs to produce another type of flip-flop circuit called a Data Latch, Delay flip-flop, D-type Bistable or simply a D-type flip-flop as it is more generally called.The D flip-flop is by far the most important of the clocked flip-flops as it ensures that ensuresthat inputs S and R are never equal to one at the same time. D-type flip-flops are constructedfrom a gated SR flip-flop with an inverter added between the S and the R inputs to allow for asingle D (data) input. This single data input D is used in place of the "set" signal, and the inverteris used to generate the complementary "reset" input thereby making a level-sensitive D-type flip-flop from a level-sensitive RS-latch as now S = D and R = not D as shown.D flip-flop CircuitWe remember that a simple SR flip-flop requires two inputs, one to "SET" the output and one to"RESET" the output. By connecting an inverter (NOT gate) to the SR flip-flop we can "SET"and "RESET" the flip-flop using just one input as now the two input signals are complements ofeach other. This complement avoids the ambiguity inherent in the SR latch when both inputs areLOW, since that state is no longer possible.Thus the single input is called the "DATA" input. If this data input is HIGH the flip-flop wouldbe "SET" and when it is LOW the flip-flop would be "RESET". However, this would be ratherpointless since the flip-flops output would always change on every data input. To avoid this anadditional input called the "CLOCK" or "ENABLE" input is used to isolate the data input fromthe flip-flop after the desired data has been stored. The effect is that D is only copied to theoutput Q when the clock is active. This then forms the basis of a D flip-flop.The D flip-flop will store and output whatever logic level is applied to its data terminal so longas the clock input is HIGH. Once the clock input goes LOW the "set" and "reset" inputs of theflip-flop are both held at logic level "1" so it will not change state and store whatever data waspresent on its output before the clock transition occurred. In other words the output is "latched"at either logic "0" or logic "1".Truth Table for the D Flip-flop
  13. 13. Clk D Q Q Description Memory ↓»0 X Q Q no change ↑»1 0 0 1 Reset Q » 0 ↑»1 1 1 0 Set Q » 1The JK Flip-flopFrom the previous tutorial we now know that the basic gated SR NAND flip-flop suffers fromtwo basic problems: number one, the S = 0 and R = 0 condition or S = R = 0 must always beavoided, and number two, if S or R change state while the enable input is high the correctlatching action may not occur. Then to overcome these two fundamental design problems withthe SR flip-flop, the JK flip-Flop was developed.This simple JK flip-Flop is the most widely used of all the flip-flop designs and is considered tobe a universal flip-flop circuit. The sequential operation of the JK flip-flop is exactly the same asfor the previous SR flip-flop with the same "Set" and "Reset" inputs. The difference this time isthat the JK flip-flop has no invalid or forbidden input states of the SR Latch (when S and R areboth 1).The JK flip-flop is basically a gated SR flip-flop with the addition of a clock input circuitry thatprevents the illegal or invalid output condition that can occur when both inputs S and R are equalto logic level "1". Due to this additional clocked input, a JK flip-flop has four possible inputcombinations, "logic 1", "logic 0", "no change" and "toggle". The symbol for a JK flip-flop issimilar to that of an SR Bistable Latch as seen in the previous tutorial except for the addition of aclock input.The Basic JK Flip-flop
  14. 14. Both the S and the R inputs of the previous SR bistable have now been replaced by two inputscalled the J and K inputs, respectively after its inventor Jack Kilby. Then this equates to: J = Sand K = R.The two 2-input AND gates of the gated SR bistable have now been replaced by two 3-inputNAND gates with the third input of each gate connected to the outputs at Q and Q. This crosscoupling of the SR flip-flop allows the previously invalid condition of S = "1" and R = "1" stateto be used to produce a "toggle action" as the two inputs are now interlocked.If the circuit is now "SET" the J input is inhibited by the"0" status of Q through the lower NAND gate. If the circuitis "RESET" the K input is inhibited by the "0" status of Qthrough the upper NAND gate. As Q and Q are alwaysdifferent we can use them to control the input. When bothinputs J and K are equal to logic "1", the JK flip-flop togglesas shown in the following truth table. The Master-Slave JKFlip-flopThe Master-Slave Flip-Flop is basically two gated SR flip-flops connected together in a seriesconfiguration with the slave having an inverted clock pulse. The outputs from Q and Q from the"Slave" flip-flop are fed back to the inputs of the "Master" with the outputs of the "Master" flip-flop being connected to the two inputs of the "Slave" flip-flop. This feedback configuration fromthe slaves output to the masters input gives the characteristic toggle of the JK flip-flop as shownbelow.The Master-Slave JK Flip-FlopThe input signals J and K are connected to the gated "master" SR flip-flop which "locks" the
  15. 15. input condition while the clock (Clk) input is "HIGH" at logic level "1". As the clock input of the"slave" flip-flop is the inverse (complement) of the "master" clock input, the "slave" SR flip-flopdoes not toggle. The outputs from the "master" flip-flop are only "seen" by the gated "slave" flip-flop when the clock input goes "LOW" to logic level "0".When the clock is "LOW", the outputs from the "master" flip-flop are latched and any additionalchanges to its inputs are ignored. The gated "slave" flip-flop now responds to the state of itsinputs passed over by the "master" section. Then on the "Low-to-High" transition of the clockpulse the inputs of the "master" flip-flop are fed through to the gated inputs of the "slave" flip-flop and on the "High-to-Low" transition the same inputs are reflected on the output of the"slave" making this type of flip-flop edge or pulse-triggered.Then, the circuit accepts input data when the clock signal is "HIGH", and passes the data to theoutput on the falling-edge of the clock signal. In other words, the Master-Slave JK Flip-flop isa "Synchronous" device as it only passes data with the timing of the clock signal.In the next tutorial about Sequential Logic Circuits, we will look at Multivibrators that are usedas waveform generators to produce the clock signals to switch sequential circuits.The Shift RegisterThe Shift Register is another type of sequential logic circuit that is used for the storage ortransfer of data in the form of binary numbers and then "shifts" the data out once every clockcycle, hence the name "shift register". It basically consists of several single bit "D-Type DataLatches", one for each bit (0 or 1) connected together in a serial or daisy-chain arrangement sothat the output from one data latch becomes the input of the next latch and so on.The data bits may be fed in or out of the register serially, i.e. one after the other from either theleft or the right direction, or in parallel, i.e. all together. The number of individual data latchesrequired to make up a single Shift Register is determined by the number of bits to be stored withthe most common being 8-bits (one byte) wide, i.e. eight individual data latches.The Shift Register is used for data storage or data movement and are used in calculators orcomputers to store data such as two binary numbers before they are added together, or to convertthe data from either a serial to parallel or parallel to serial format. The individual data latches thatmake up a single shift register are all driven by a common clock ( Clk ) signal making themsynchronous devices.Shift register ICs are generally provided with a clear or reset connection so that they can be"SET" or "RESET" as required. Generally, shift registers operate in one of four different modeswith the basic movement of data through a shift register being:
  16. 16. Serial-in to Parallel-out (SIPO) - the register is loaded with serial data, one bit at a time, with the stored data being available in parallel form. Serial-in to Serial-out (SISO) - the data is shifted serially "IN" and "OUT" of the register, one bit at a time in either a left or right direction under clock control. Parallel-in to Serial-out (PISO) - the parallel data is loaded into the register simultaneously and is shifted out of the register serially one bit at a time under clock control. Parallel-in to Parallel-out (PIPO) - the parallel data is loaded simultaneously into the register, and transferred together to their respective outputs by the same clock pulse.The effect of data movement from left to right through a shift register can be presentedgraphically as:Also, the directional movement of the data through a shift register can be either to the left, (leftshifting) to the right, (right shifting) left-in but right-out, (rotation) or both left and right shiftingwithin the same register thereby making it bidirectional. In this tutorial it is assumed that all thedata shifts to the right, (right shifting).Serial-in to Parallel-out (SIPO)4-bit Serial-in to Parallel-out Shift Register
  17. 17. The operation is as follows. Lets assume that all the flip-flops ( FFA to FFD ) have just beenRESET ( CLEAR input ) and that all the outputs QA to QD are at logic level "0" i.e, no paralleldata output. If a logic "1" is connected to the DATA input pin of FFA then on the first clockpulse the output of FFA and therefore the resulting QA will be set HIGH to logic "1" with all theother outputs still remaining LOW at logic "0". Assume now that the DATA input pin of FFAhas returned LOW again to logic "0" giving us one data pulse or 0-1-0.The second clock pulse will change the output of FFA to logic "0" and the output of FFB and QBHIGH to logic "1" as its input D has the logic "1" level on it from QA. The logic "1" has nowmoved or been "shifted" one place along the register to the right as it is now at QA. When thethird clock pulse arrives this logic "1" value moves to the output of FFC ( QC ) and so on untilthe arrival of the fifth clock pulse which sets all the outputs QA to QD back again to logic level"0" because the input to FFA has remained constant at logic level "0".The effect of each clock pulse is to shift the data contents of each stage one place to the right,and this is shown in the following table until the complete data value of 0-0-0-1 is stored in theregister. This data value can now be read directly from the outputs of QA to QD. Then the datahas been converted from a serial data input signal to a parallel data output. The truth table andfollowing waveforms show the propagation of the logic "1" through the register from left to rightas follows.Basic Movement of Data through a Shift Register Clock Pulse No QA QB QC QD 0 0 0 0 0 1 1 0 0 0 2 0 1 0 0 3 0 0 1 0 4 0 0 0 1 5 0 0 0 0
  18. 18. Note that after the fourth clock pulse has ended the 4-bits of data ( 0-0-0-1 ) are stored in theregister and will remain there provided clocking of the register has stopped. In practice the inputdata to the register may consist of various combinations of logic "1" and "0". Commonlyavailable SIPO ICs include the standard 8-bit 74LS164 or the 74LS594.Serial-in to Serial-out (SISO)This shift register is very similar to the SIPO above, except were before the data was readdirectly in a parallel form from the outputs QA to QD, this time the data is allowed to flowstraight through the register and out of the other end. Since there is only one output, the DATAleaves the shift register one bit at a time in a serial pattern, hence the name Serial-in to Serial-Out Shift Register or SISO.The SISO shift register is one of the simplest of the four configurations as it has only threeconnections, the serial input (SI) which determines what enters the left hand flip-flop, the serialoutput (SO) which is taken from the output of the right hand flip-flop and the sequencing clocksignal (Clk). The logic circuit diagram below shows a generalized serial-in serial-out shiftregister.4-bit Serial-in to Serial-out Shift Register
  19. 19. You may think whats the point of a SISO shift register if the output data is exactly the same asthe input data. Well this type of Shift Register also acts as a temporary storage device or as atime delay device for the data, with the amount of time delay being controlled by the number ofstages in the register, 4, 8, 16 etc or by varying the application of the clock pulses. Commonlyavailable ICs include the 74HC595 8-bit Serial-in/Serial-out Shift Register all with 3-stateoutputs.Parallel-in to Serial-out (PISO)The Parallel-in to Serial-out shift register acts in the opposite way to the serial-in to parallel-outone above. The data is loaded into the register in a parallel format i.e. all the data bits enter theirinputs simultaneously, to the parallel input pins PA to PD of the register. The data is then read outsequentially in the normal shift-right mode from the register at Q representing the data present atPA to PD.This data is outputted one bit at a time on each clock cycle in a serial format. It is important tonote that with this system a clock pulse is not required to parallel load the register as it is alreadypresent, but four clock pulses are required to unload the data.4-bit Parallel-in to Serial-out Shift RegisterAs this type of shift register converts parallel data, such as an 8-bit data word into serial format,it can be used to multiplex many different input lines into a single serial DATA stream whichcan be sent directly to a computer or transmitted over a communications line. Commonlyavailable ICs include the 74HC166 8-bit Parallel-in/Serial-out Shift Registers.
  20. 20. Parallel-in to Parallel-out (PIPO)The final mode of operation is the Parallel-in to Parallel-out Shift Register. This type of registeralso acts as a temporary storage device or as a time delay device similar to the SISOconfiguration above. The data is presented in a parallel format to the parallel input pins PA to PDand then transferred together directly to their respective output pins QA to QA by the same clockpulse. Then one clock pulse loads and unloads the register. This arrangement for parallel loadingand unloading is shown below.4-bit Parallel-in to Parallel-out Shift RegisterThe PIPO shift register is the simplest of the four configurations as it has only three connections,the parallel input (PI) which determines what enters the flip-flop, the parallel output (PO) and thesequencing clock signal (Clk).Similar to the Serial-in to Serial-out shift register, this type of register also acts as a temporarystorage device or as a time delay device, with the amount of time delay being varied by thefrequency of the clock pulses. Also, in this type of register there are no interconnections betweenthe individual flip-flops since no serial shifting of the data is required.Asynchronous Counter
  21. 21. In the previous tutorial we saw that an Asynchronous counter can have 2n-1 possible countingstates e.g. MOD-16 for a 4-bit counter, (0-15) making it ideal for use in Frequency Division. Butit is also possible to use the basic asynchronous counter to construct special counters withcounting states less than their maximum output number by forcing the counter to reset itself tozero at a pre-determined value producing a type of asynchronous counter that has truncatedsequences. Then an n-bit counter that counts up to its maximum modulus (2n) is called a fullsequence counter and a n-bit counter whose modulus is less than the maximum possible is calleda truncated counter.But why would we want to create an asynchronous truncated counter that is not a MOD-4,MOD-8, or some other modulus that is equal to the power of two. The answer is that we can byusing combinational logic to take advantage of the asynchronous inputs on the flip-flop. If wetake the modulo-16 asynchronous counter and modified it with additional logic gates it can bemade to give a decade (divide-by-10) counter output for use in standard decimal counting andarithmetic circuits.Such counters are generally referred to as Decade Counters. A decade counter requires resettingto zero when the output count reaches the decimal value of 10, ie. when DCBA = 1010 and to dothis we need to feed this condition back to the reset input. A counter with a count sequence frombinary "0000" (BCD = "0") through to "1001" (BCD = "9") is generally referred to as a BCDbinary-coded-decimal counter because its ten state sequence is that of a BCD code but binarydecade counters are more common.Asynchronous Decade CounterThis type of asynchronous counter counts upwards on each leading edge of the input clock signalstarting from "0000" until it reaches an output "1010" (decimal 10). Both outputs QB and QD arenow equal to logic "1" and the output from the NAND gate changes state from logic "1" to alogic "0" level and whose output is also connected to the CLEAR (CLR) inputs of all the J-KFlip-flops.
  22. 22. This signal causes all of the Q outputs to be reset back to binary "0000" on the count of 10. OnceQB and QD are both equal to logic "0" the output of the NAND gate returns back to a logic level"1" and the counter restarts again from "0000". We now have a decade or Modulo-10 counter.Decade Counter Truth Table Clock Output bit Pattern Decimal Count QD QC QB QA Value 1 0 0 0 0 0 2 0 0 0 1 1 3 0 0 1 0 2 4 0 0 1 1 3 5 0 1 0 0 4 6 0 1 0 1 5 7 0 1 1 0 6 8 0 1 1 1 7 9 1 0 0 0 8 10 1 0 0 1 9 11 Counter Resets its Outputs back to ZeroDecade Counter Timing DiagramUsing the same idea of truncating counter output sequences, the above circuit could easily be
  23. 23. adapted to other counting cycles be simply changing the connections to the AND gate. Forexample, a scale-of-twelve (modulo-12) can easily be made by simply taking the inputs to theAND gate from the outputs at "QC" and "QD", noting that the binary equivalent of 12 is "1100"and that output "QA" is the least significant bit (LSB).Since the maximum modulus that can be implemented with n flip-flops is 2n, this means thatwhen you are designing truncated asynchronous counters you should determine the lowest powerof two that is greater than or equal to your desired modulus. For example, lets say you wish tocount from 0 to 39, or mod-40. Then the highest number of flip-flops required would be six, n =6 giving a maximum MOD of 64 as five flip-flops wouldonly equal MOD-32.Now suppose we wanted to build a "divide-by-128"counter for frequency division we would need to cascadeseven flip-flops since 128 = 27. Using dual flip-flopssuch as the 74LS74 we would still need four ICs tocomplete the circuit.One easy alternative method would be to use two TTL7493s as 4-bit ripple counter/dividers. Since 128 = 16 x 8, one 7493 could be configured as a"divide-by-16" counter and the other as a "divide-by-8" counter. The two ICs would be cascadedtogether to form a "divide-by-128" frequency divider as shown.Of course standard IC asynchronous counters are available such as the TTL 74LS90programmable ripple counter/divider which can be configured as a divide-by-2, divide-by-5 orany combination of both. The 74LS390 is a very flexible dual decade driver IC with a largenumber of "divide-by" combinations available ranging form divide-by-2, 4, 5, 10, 20, 25, 50, and100Binary Synchronous CounterIn the previous Asynchronous binary counter tutorial, we saw that the output of one counterstage is connected directly to the clock input of the next counter stage and so on along the chain,and as a result the asynchronous counter suffers from what is known as "Propagation Delay" inwhich the timing signal is delayed a fraction through each flip-flop.However, with the Synchronous Counter, the external clock signal is connected to the clockinput of EVERY individual flip-flop within the counter so that all of the flip-flops are clockedtogether simultaneously (in parallel) at the same time giving a fixed time relationship. In otherwords, changes in the output occur in "synchronization" with the clock signal. This results in allthe individual output bits changing state at exactly the same time in response to the commonclock signal with no ripple effect and therefore, no propagation delay.Binary 4-bit Synchronous Counter
  24. 24. It can be seen that the external clock pulses (pulses to be counted) are fed directly to each J-Kflip-flop in the counter chain and that both the J and K inputs are all tied together in toggle mode,but only in the first flip-flop, flip-flop A (LSB) are they connected HIGH, logic "1" allowing theflip-flop to toggle on every clock pulse. Then the synchronous counter follows a predeterminedsequence of states in response to the common clock signal, advancing one state for each pulse.The J and K inputs of flip-flop B are connected to the output "Q" of flip-flop A, but the J and Kinputs of flip-flops C and D are driven from AND gates which are also supplied with signalsfrom the input and output of the previous stage. If we enable each J-K flip-flop to toggle basedon whether or not all preceding flip-flop outputs (Q) are "HIGH" we can obtain the samecounting sequence as with the asynchronous circuit but without the ripple effect, since each flip-flop in this circuit will be clocked at exactly the same time. As there is no propagation delay insynchronous counters because all the counter stages are triggered in parallel the maximumoperating frequency of this type of counter is much higher than that of a similar asynchronouscounter.4-bit Synchronous Counter Waveform Timing Diagram.
  25. 25. Because this 4-bit synchronous counter counts sequentially on every clock pulse the resultingoutputs count upwards from 0 ( "0000" ) to 15 ( "1111" ). Therefore, this type of counter is alsoknown as a 4-bit Synchronous Up Counter.As synchronous counters are formed by connecting flip-flops together and any number of flip-flops can be connected or "cascaded" together to form a "divide-by-n" binary counter, themodulos or "MOD" number still applies as it does for asynchronous counters so a Decadecounter or BCD counter with counts from 0 to 2n-1 can be built along with truncated sequences.Combinational Logic CircuitsUnlike Sequential Logic Circuits whose outputs are dependant on both their present inputs andtheir previous output state giving them some form of Memory, the outputs of CombinationalLogic Circuits are only determined by the logical function of their current input state, logic "0"or logic "1", at any given instant in time as they have no feedback, and any changes to the signalsbeing applied to their inputs will immediately have an effect at the output. In other words, in aCombinational Logic Circuit, the output is dependant at all times on the combination of itsinputs and if one of its inputs condition changes state so does the output as combinational circuitshave "no memory", "timing" or "feedback loops".Combinational Logic
  26. 26. Combinational Logic Circuits are made up from basic logic NAND, NOR or NOT gates that are"combined" or connected together to produce more complicated switching circuits. These logicgates are the building blocks of combinational logic circuits. An example of a combinationalcircuit is a decoder, which converts the binary code data present at its input into a number ofdifferent output lines, one at a time producing an equivalent decimal code at its output.Combinational logic circuits can be very simple or very complicated and any combinationalcircuit can be implemented with only NAND and NOR gates as these are classed as "universal"gates.The three main ways of specifying the function of a combinational logic circuit are: 1. Boolean Algebra – This forms the algebraic expression showing the operation of the logic circuit for each input variable either True or False that results in a logic "1" output. 2. Truth Table – A truth table defines the function of a logic gate by providing a concise list that shows all the output states in tabular form for each possible combination of input variable that the gate could encounter. 3. Logic Diagram – This is a graphical representation of a logic circuit that shows the wiring and connections of each individual logic gate, represented by a specific graphical symbol, that implements the logic circuit.and all three of these logic circuit representations are shown below.
  27. 27. As combinational logic circuits are made up from individual logic gates only, they can also beconsidered as "decision making circuits" and combinational logic is about combining logic gatestogether to process two or more signals in order to produce at least one output signal accordingto the logical function of each logic gate. Common combinational circuits made up fromindividual logic gates that carry out a desired application include Multiplexers, De-multiplexers, Encoders, Decoders, Full and Half Adders etc.Classification of Combinational LogicOne of the most common uses of combinational logic is in Multiplexer and De-multiplexer typecircuits. Here, multiple inputs or outputs are connected to a common signal line and logic gates
  28. 28. are used to decode an address to select a single data input or output switch. A multiplexer consistof two separate components, a logic decoder and some solid state switches, but before we candiscuss multiplexers, decoders and de-multiplexers in more detail we first need to understandhow these devices use these "solid state switches" in their design.The Half Adder CircuitAnother common and very useful combinational logic circuit which can be constructed using justa few basic logic gates and adds together binary numbers is the Binary Adder circuit. TheBinary Adder is made up from standard AND and Ex-OR gates and allow us to "add" togethersingle bit binary numbers, a and b to produce two outputs called the SUM of the addition and aCARRY called the Carry-out, ( C out ) bit. One of the main uses for the Binary Adder is inarithmetic and counting circuits.Consider the addition of two denary (base 10) numbers below. 123 A (Augend) + 789 B (Addend) 912 SUMEach column is added together starting from the right hand side and each digit has a weightedvalue depending upon its position in the columns. As each column is added together a carry isgenerated if the result is greater or equal to ten, the base number. This carry is then added to theresult of the addition of the next column to the left and so on, simple school maths addition. Theadding of binary numbers is basically the same as that of adding decimal numbers but this time acarry is only generated when the result in any column is greater or equal to "2", the base numberof binary.1-bit Adder with Carry-Out Symbol Truth Table A B SUM CARRY 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 Boolean Expression: Sum = A ⊕ B Carry = A . B
  29. 29. From the truth table we can see that the SUM (S) output is the result of the Ex-OR gate and theCarry-out (Cout) is the result of the AND gate. One major disadvantage of the Half Adder circuitwhen used as a binary adder, is that there is no provision for a "Carry-in" from the previouscircuit when adding together multiple data bits.For example, suppose we want to add together two 8-bit bytes of data, any resulting carry bitwould need to be able to "ripple" or move across the bit patterns starting from the leastsignificant bit (LSB). The most complicated operation the half adder can do is "1 + 1" but as thehalf adder has no carry input the resultant added value would be incorrect. One simple way toovercome this problem is to use a Full Adder type binary adder circuit.The Full Adder CircuitThe main difference between the Full Adder and the previous seen Half Adder is that a fulladder has three inputs, the same two single bit binary inputs A and B as before plus an additionalCarry-In (C-in) input as shown below.Full Adder with Carry-In Symbol Truth Table A B C-in Sum C-out 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 Boolean Expression: Sum = A ⊕ B ⊕ C-inThe 1-bit Full Adder circuit above is basically two half adders connected together and consistsof three Ex-OR gates, two AND gates and an OR gate, six logic gates in total. The truth table forthe full adder includes an additional column to take into account the Carry-in input as well as thesummed output and carry-output. 4-bit full adder circuits are available as standard IC packagesin the form of the TTL 74LS83 or the 74LS283 which can add together two 4-bit binary numbersand generate a SUM and a CARRY output. But what if we wanted to add together two n-bitnumbers, then n 1-bit full adders need to be connected together to produce what is known as theRipple Carry Adder.
  30. 30. The 4-bit Binary AdderThe Ripple Carry Binary Adder is simply n, full adders cascaded together with each full adderrepresents a single weighted column in the long addition with the carry signals producing a"ripple" effect through the binary adder from right to left. For example, suppose we want to"add" together two 4-bit numbers, the two outputs of the first full adder will provide the firstplace digit sum of the addition plus a carry-out bit that acts as the carry-in digit of the next binaryadder.The second binary adder in the chain also produces a summed output (the 2nd bit) plus anothercarry-out bit and we can keep adding more full adders to the combination to add larger numbers,linking the carry bit output from the first full binary adder to the next full adder, and so forth. Anexample of a 4-bit adder is given below.A 4-bit Binary AdderOne main disadvantage of "cascading" together 1-bit binary adders to add large binary numbersis that if inputs A and B change, the sum at its output will not be valid until any carry-input has"rippled" through every full adder in the chain. Consequently, there will be a finite delay beforethe output of a adder responds to a change in its inputs resulting in the accumulated delayespecially in large multi-bit binary adders becoming prohibitively large. This delay is calledPropagation delay. Also "overflow" occurs when an n-bit adder adds two numbers togetherwhose sum is greater than or equal to 2nOne solution is to generate the carry-input signals directly from the A and B inputs rather thanusing the ripple arrangement above. This then produces another type of binary adder circuitcalled a Carry Look Ahead Binary Adder were the speed of the parallel adder can be greatlyimproved using carry-look ahead logic.