Module 4 Logic Circuits.pptx
- 12. Introduction The logic circuits are used extensively in digital systems and form the basis of clocks, counters, shift registers and timers. Some basic logic gate like NOT, AND, OR, the special logic gates like Exclusive-OR, Exclusive NOR and universal logic gate like NAND and NOR are introduced. Their symbols, truth table are that describes their operations are explained. Further, it has been explained to construct a combinational logic circuits using above gates and also about how to identify the digital devices according to semiconductor technology-TTL or CMOS.
- 13. Logic functions Electronic logic circuits can be used to make simple decisions like: 1) If dark then put on the light. 2) If temperature is less then 20°C then connect the supply to the heater. They can also be used to make more complex decisions like: If ‘hour’ is greater than 11 and ‘24 hour clock’ is not selected then display message ‘pm’.
- 14. Logic functions All of these logical statements are similar in form. The first two are essentially: If {condition} then {action}. while the third is a compound statement of the form: If {condition 1} and not {condition 2} then {action}. Both of these statements can be readily implemented using straightforward electronic circuits. Because this circuitry is based on discrete states and since the behavior of the circuits can be described by a set of logical statements, it is referred to as digital logic.
- 15. Switch and lamp logic In the simple circuit shown in Figure 4.1 a battery is connected to a lamp via a switch. There are two possible states for the switch, open and close. Lamp will only operate when the switch is closed. The logical state of the switch can be represented by the binary digits, 0 and 1. That is, if logical 0 is synonymous with open (or ‘off’) and logical 1 is equivalent to closed (or ‘on’), then: Switch open (off) = 0 Switch closed (on) = 1
- 16. Switch and lamp logic Figure 4.1 Simple switch and lamp circuit Condition Switch Comment 1 Open No light produced 2 Closed Light produced Table 4.1 Simple switching logic Figure 4.2 Truth table for the switch and lamp
- 17. AND logic Figure 4.3 AND switch and lamp logic Table 4.2 Simple AND switching logic Table 4.3 Truth table for the AND logic Condition Switch A Switch B Comment 1 Open Open No light produced 2 Open Closed No light produced 3 Closed Open No light produced 4 Closed Closed Light produced
- 18. AND logic The AND function is explained once again by using the simple switch and light system as shown in Figure 4.3. The related circuit can be easily understood through truth table shown in Table 4.2. Here the lamp will only operate when switch A is closed and switch B is closed. Since there are two switches (A and B) and there are two possible states for each switch (open or closed), there is a total of four possible conditions for the circuit. Each switch can only be in one of the two states (i.e. open or closed) at any given time, the open and closed conditions are mutually exclusive.
- 19. AND logic Furthermore, since the switches cannot exist in any other state than completely open or completely closed (i.e. there are no intermediate states) the circuit uses binary logic. We can thus represent the logical states of the two switches by the binary digits, 0 and 1. Once again, if we adopt the convention that an open switch can be represented by 0 and a closed switch by 1, we can rewrite the truth table in terms of the binary states shown in table 4.3 where: No light (off) = 0 Light (on) = 1
- 20. OR logic Figure 4.4 OR switch and lamp logic Table 4.2 Simple OR switching logic Table 4.5 Truth table for OR logic Condition Switch A Switch B Comment 1 Open Open No light produced 2 Open Closed Light produced 3 Closed Open Light produced 4 Closed Closed Light produced A B Y 0 0 0 0 1 1 1 0 1 1 1 1
- 21. OR logic Figure 4.4 shows another circuit with two switches. This circuit differs from that shown in Figure 4.3 by virtue of the fact that the two switches are connected in parallel rather than in series. In this case the lamp will operate when either of the two switches is closed. There are four possible conditions for the circuit. We can summarize these conditions in Table 4.4. Once again, adopting the convention that an open switch can be represented by 0 and a closed switch by 1, we can rewrite the truth table in terms of the binary states as shown in Table 4.5.
- 22. Logic gates Logic gates are circuits designed to produce the basic logic functions, AND, OR, etc. These circuits are designed to be interconnected into larger, more complex, logic circuit arrangements. Since these circuits form the basic building blocks of all digital systems, we have summarized the action of each of the gates in the next section. For each gate we have included its British Standard (BS) symbol together with its American Standard (MIL/ANSI) symbol. We have also included the truth tables and Boolean expressions (using ‘+’ to denote OR, ‘·’ to denote AND, and ‘E’ to denote NOT). Note that, while inverters and buffers each have only one input, exclusive- OR gates have two inputs and the other basic gates (AND, OR, NAND and
- 23. Buffers Buffers do not affect the logical state of a digital signal (i.e. a logic 1 input results in a logic 1 output whereas a logic 0 input results in a logic 0 output). Buffers are normally used to provide extra current drive at the output but can also be used to regularize the logic levels present at an interface. The Boolean expression for the output, Y, of a buffer with an input, X, is: Y = X. Figure 4.5 Symbols and truth table for a buffer
- 24. Inverters Inverters are used to complement the logical state (i.e. a logic 1 input results in a logic 0 output and vice versa). Inverters also provide extra current drive and, like buffers, are used in interfacing applications where they provide a means of regularizing logic levels present at the input or output of a digital system. The Boolean expression for the output, Y, of a inverter with an input, X, is: Y =X Figure 4.6 Symbols and truth table for an Inverter
- 25. AND gate AND gates will only produce a logic 1 output when all inputs are simultaneously at logic 1. Any other input combination results in a logic 0 output. The Boolean expression for the output, Y, of an AND gate with inputs, A and B, is: Y =A.B Figure 4.7 Symbols and truth table for an AND Gate
- 26. OR gate OR gates will produce a logic 1 output whenever anyone, or more, inputs are at logic 1. Putting this in another way, an OR gate will only produce a logic 0 output whenever all of its inputs are simultaneously at logic 0. The Boolean expression for the output, Y, of an OR gate with inputs, A and B, is: Y =A+B Figure 4.8 Symbols and truth table for an OR Gate
- 27. NAND gate NAND (i.e. NOT-AND) gates will only produce a logic 0 output when all inputs are simultaneously at logic 1. Any other input combination will produce a logic 1 output. A NAND gate, therefore, is nothing more than an AND gate with its output inverted! The circle shown at the output denotes this inversion. The Boolean expression for the output, Y, of a NAND gate with inputs, A and B, is: Y =A.B Figure 4.9 Symbols and truth table for a NAND Gate
- 28. NOR gate NOR (i.e. NOT-OR) gates will only produce a logic 1 output when all inputs are simultaneously at logic 0. Any other input combination will produce a logic 0 output. A NOR gate, therefore, is simply an OR gate with its output inverted. A circle is again used to indicate inversion. The Boolean expression for the output, Y, of a NOR gate with inputs, A and B, is: Y =A+B Figure 4.10 Symbols and truth table for a NOR Gate
- 29. Exclusive-OR gates Exclusive-OR gates will produce a logic 1 output whenever either one of the inputs is at logic 1 and the other is at logic 0. Exclusive-OR gates produce a logic 0 output whenever both inputs have the same logical state (i.e. when both are at logic 0 or both are at logic 1). The Boolean expression for the output, Y, of an exclusive-OR gate with inputs, A and B, is: Y =A.B+B.A Figure 4.11 Symbols and truth table for an exclusive-OR gate
- 30. Combinational logic By using a standard range of logic levels (i.e. voltage levels used to represent the logic 1 and logic 0 states) logic circuits can be combined together in order to solve complex logic functions. The output of a bistable has two stables states (logic 0 or logic 1) and, once set in one or other of these states, the device will remain at a particular logic level for an indefinite period until reset. A bistable thus constitutes a simple form of ‘memory cell’ because it will remain in its latched state (whether set or reset) until a signal is applied to it in order to change its state (or until the supply is disconnected).
- 76. Bistables Figure 4.12 R-S bistables using cross-coupled NAND and NOR gates
- 78. R-S bistables The simplest form of bistable is the R-S bistable. This device has two inputs, SET and RESET, and complementary outputs, Q and Q. A logic 1 applied to the SET input will cause the Q output to become (or remain at) logic 1 while a logic 1 applied to the RESET input will cause the Q output to become (or remain at) logic 0. In either case, the bistable will remain in its SET or RESET state until an input is applied in such a sense as to change the state. Two simple forms of R-S bistable based on cross-coupled logic gates are shown in Figure 4.12. Figure 4.12(a) is based on NAND gates while Figure 4.12(b) is based on NOR gates. The simple cross-coupled logic gate bistable has a number of serious shortcomings (consider what would happen if a logic 1 was simultaneously present on both the SET and RESET inputs!) and practical forms of bistable make use of much improved purpose-designed logic circuits such as D-type and
- 79. D-type bistables The D-type bistable has two inputs: D (standing variously for ‘data’ or ‘delay’) and CLOCK (CLK). The data input (logic 0 or logic 1) is clocked into the bistable such that the output state only changes when the clock changes state. Operation is thus said to be synchronous. Additional subsidiary inputs (which are invariably active low) are provided which can be used to directly set or reset the bistable. These are usually called PRESET (PR) and CLEAR (CLR). D-type bistables are used both as latches (a simple form of memory) and as binary dividers.
- 80. D-type bistables Figure 4.13 D-type bistable operation
- 81. D-type bistables Figure D-type bistable Symbol and Circuit
- 82. D-type bistables – Timing diagram Figure 4.14 Timing diagram for the D-type Bistable
- 83. J-K bistables J-K bistables have two clocked inputs (J and K), two direct inputs (PRESET and CLEAR), a CLOCK (CK) input, and outputs (Q and Q). As with R-S bistables, the two outputs are complementary (i.e. when one is 0 the other is 1, and vice versa). Similarly, the PRESET and CLEAR inputs are invariably both active low (i.e. a 0 on the PRESET input will set the Q output to 1 whereas a 0 on the CLEAR input will set the Q output to 0). Tables 4.6 and 4.7 summarize the operation of a J-K bistable respectively for the PRESET and CLEAR inputs and for clocked operation.
- 84. J-K bistables
- 85. The Truth Table for the JK Function
- 86. J-K bistables Figure 4.15 Four-stage binary counter using J-K bistables
- 87. J-K bistables Figure 4.16 Timing diagram for the four-stage binary counter shown in Figure 4.15
- 88. J-K bistables Table 4.6 Input and output states for a J-K bistable (PRESET and CLEAR inputs) Inputs Output (QN+1) Comments PRESET CLEAR 0 0 ? Indeterminate 0 1 0 Q output changes to 0 (i.e. Q is reset) regardless of the clock state 1 0 1 Q output changes to 1 (i.e. Q is set) regardless of the clock state 1 1 See below operation (refer to Table 4.7) Note: The preset and clear inputs operate regardless of the clock.
- 89. J-K bistables Table 4.7 Input and output states for a J-K bistable (clocked operation) Inputs Output (QN+1) Comments J K 0 0 QN No change in state of the Q output on the next clock transition 0 1 0 Q output changes to 0 (i.e. Q is reset) on the next clock transition 1 0 1 Q output changes to 1 (i.e. Q is set) on the next clock transition 1 1 QN Q output changes to the opposite state on the next clock transition Note: QN+1 means ‘Q after the next clock transition’ while QN means ‘Q in whatever state it was before’.
- 90. J-K bistables Figure JK bistable Symbol and Circuit
- 91. J-K bistables J-K bistables are the most sophisticated and flexible of the bistable types and they can be configured in various ways including binary dividers, shift registers, and latches. Figure 4.15 shows the arrangement of a four stage binary counter based on J-K bistables. The timing diagram for this circuit is shown in Figure 4.16. Each stage successively divides the clock input signal by a factor of two. Note that a logic 1 input is transferred to the respective Q-output on the falling edge of the clock pulse and all J and K inputs must be taken to logic 1 to enable binary counting. Figure 4.17 shows the arrangement of a four stage shift register based on J-K bistables. The timing diagram for this circuit is shown in Figure 4.18. Note that each stage successively feeds data to the next stage. Note that all data transfer
- 92. J-K bistables Figure 4.17 Four-stage shift register using J-K bistables
- 93. J-K bistables Figure 4.18 Timing diagram for the four-stage shift register shown in Figure 4.17
- 94. Integrated circuit logic devices The task of realizing a complex logic circuit is made simple with the aid of digital integrated circuits. Such devices are classified according to the semiconductor technology used in their fabrication (the logic family to which a device belongs is largely instrumental in determining its operational characteristics, such as power consumption, speed and immunity to noise). The relative size of a digital integrated circuit (in terms of the number of active devices that it contains) is often referred to as its scale of integration and the terminology in Table 4.8 is commonly used.
- 95. Integrated circuit logic devices Table 4.8 Scale of integration Scale of integration Abbreviation Number of logic gates* Small SSI 1 to 10 Medium MSI 10 to 100 Large LSI 100 to 1,000 Very large VLSI 1,000 to 10,000 Super large SLSI SLSI 10,000 to 100,000 * or active circuitry of equivalent complexity
- 96. Integrated circuit logic devices The two basic logic families are CMOS (complementary metal oxide semiconductor) and TTL (transistor transistor logic). Each of these families is then further sub-divided. The most common family of TTL logic devices is known as the 74-series. Devices from this family are coded with the prefix number 74. Variants within the family are identified by letters which follow the initial 74 prefix, as shown in Table 4.9. The most common family of CMOS devices is known as the 4000- series. Variants within the family are identified by the suffix letters given in Table 4.10.
- 97. Integrated circuit logic devices Table 4.9 TTL device coding - infix letters Infix Meaning None Standard TTL device ALS Advanced low-power Schottky C CMOS version of a TTL device F ‘Fast’ (a high-speed version) H High-speed version S Schottky input configuration (improved speed and noise immunity) HC High-speed CMOS version (CMOS compatible inputs) HCT HCT High-speed CMOS version (TTL compatible inputs) LS Low-power Schottky
- 98. Integrated circuit logic devices Table 4.10 CMOS device coding the most common variants of the 4000 family are identified using these suffix letters Infix Meaning A Standard CMOS device None Standard (unbuffered) CMOS device B, BE Improved (buffered) CMOS device UB, UBE Improved (unbuffered) CMOS device
- 99. Thank you for listening
- 100. Inside a AND gate
- 101. Inside a OR gate