# DIGITAL CIRCUIT LOGIC UNIT 9: MULTIPLEXERS, DECODERS, AND PROGRAMMABLE LOGIC DEVICES

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1 DIGITAL CIRCUIT LOGIC UNIT 9: MULTIPLEXERS, DECODERS, AND PROGRAMMABLE LOGIC DEVICES 1

2 Learning Objectives 1. Explain the function of a multiplexer. Implement a multiplexer using gates. 2. Explain the operation of three-state buffers. Determine the resulting output when three-state buffer outputs are connected together. Use three-state buffers to multiplex signals onto a bus. 3. Explain the operation of a decoder and encoder. Use a decoder with added gates to implement a set of logic functions. Implement a decoder or priority encoder using gates. 4. Explain the operation of a read-only memory (ROM). Use a ROM to implement a set of logic functions. 2

3 Learning Objectives 5. Explain the operation of a programmable logic array (PLA). Use a PLA to implement a set of logic functions. Given a PLA table or an internal connection diagram for a PLA, determine the logic functions realized. 6. Explain the operation of a programmable array logic device (PAL). Determine the programming pattern required to realize a set of logic functions with a PAL. 7. Explain the operation of a complex programmable logic device (CPLD) and a field-programmable gate array (FPGA). 8. Use Shannon s expansion theorem to decompose a switching function. 3

4 Introduction Introduction: In this unit we introduce the use of more complex integrated circuits (ICs) in logic design. Integrated circuits may be classified as small-scale integration (SSI), medium-scale integration (MSI), large-scale integration (LSI), or very-large-scale integration (VLSI), depending on the number of gates in each integrated circuit package and the type of function performed. SSI functions include NAND, NOR, AND, and OR gates, inverters, and flip-flops. 4

5 Decoders and Encoders 3-8 Decoder Block Diagram and Truth Table: 5

6 Decoders and Encoders 4-10 Line Decoder Logic Diagram: 6

7 Decoders and Encoders 4-10 Decoder Block Diagram and Truth Table: 7

8 Decoders and Encoders General Line Decoder Output Equations: 8

9 Decoders and Encoders Realization of Functions Using Decoders: For functions f1 and f2: 9

10 iclicker Question 15 What type of logic gate (single gate) is required at the decoder output to realize f1 and f2? (1 minute) A) OR B) AND C) XOR D) NOR E) NAND 10

11 Decoders and Encoders Realization of Functions Using Decoders: For functions f1 and f2: 11

12 Decoders and Encoders Realization of Functions Using Decoders: For functions f1 and f2: 12

13 Decoders and Encoders Encoders: Encoders have the inverse function of decoders. 13

14 Read-Only Memories Read-Only Memory: A read-only memory (ROM) consists of an array of semiconductor devices that are interconnected to store an array of binary data. Once binary data is stored in the ROM, it can be read out whenever desired, but the data that is stored cannot be changed under normal operating conditions. 14

15 Read-Only Memories ROM with n-inputs and m-outputs: A ROM which has n input lines and m output lines (Figure 9-22) contains an array of 2 n words, and each word is m bits long. The input lines serve as an address to select one of the 2 n words. When an input combination is applied to the ROM, the pattern of 0 s and 1 s which is stored in the corresponding word in the memory appears at the output lines. A 2 n m ROM can realize m functions of n variables because it can store a truth table with 2 n rows and m columns. 15

16 Read-Only Memories Basic ROM Structure: A ROM basically consists of a decoder and a memory array, as shown in Figure When a pattern of n 0 s and 1 s is applied to the decoder inputs, exactly one of the 2 n decoder outputs is 1. This decoder output line selects one of the words in the memory array, and the bit pattern stored in this word is transferred to the memory output lines. 16

17 Read-Only Memories 8-Word x 4-Bit ROM: 17

18 Read-Only Memories 8-Word by 4-Bit ROM Functions: 18

19 Read-Only Memories Hexadecimal-to-ASCII Code Converter: 19

20 Read-Only Memories ROM Realization of Code Converter: 20

21 Multiplexers Multiplexers: A multiplexer (or data selector, abbreviated as MUX) has a group of data inputs and a group of control inputs. The control inputs are used to select one of the data inputs and connect it to the output terminal. A 2-1 MUX and its logic equation are shown below: 21

22 Multiplexers More Multiplexers: Logic Equation for 4-1 MUX: Logic Equation for 8-1 MUX: Logic Equation for 2 n -1 MUX: 22

23 Multiplexers Logic Diagram for 8-to-1 MUX: 23

24 Multiplexers 8-to-1 MUX NAND Implementation: NAND Logic Equation from Factoring Equation 9-2: 24

25 Multiplexers Quad Multiplexers to Select Data: Multiplexers are often used to select data which is to be processed or stored in digital system design. 25

26 Multiplexers Enable: Another type of multiplexer has an additional input called an enable. (sometimes asynchronous) The 8-to-1 MUX in Figure 9-3 can be modified to include an enable by changing the AND gates to fiveinput gates. The enable signal E is connected to the fifth input of each of the AND gates. Then, if E = 0, Z = 0 independent of the gate inputs Ii and the select inputs a, b, and c. However, if E = 1, then the MUX functions as an ordinary 8-to-1 multiplexer. 26

27 Multiplexers 4-1 Multiplexer Combinations and Implemented Functions: 27

28 Three-State Buffers Buffers: A gate output can only be connected to a limited number of other device inputs without degrading the digital system s performance. A simple buffer may be used to increase the driving capability of a gate output. Figure 9-10 shows a buffer connected between a gate output and several gate inputs. Because no bubble is present 28

29 Three-State Buffers Four Kinds of Three State- Buffers: 29

30 Three-State Buffers Data Selection and Circuits with Three-State Buffers: 30

31 Three-State Buffers 4-Bit Adder and Bidirectional Input-Outputs: Bi-directional means that the same pin can be used as an input pin and as an output pin, but not both at the same time. 31

32 Programmable Logic Devices A programmable logic device (or PLD) is a general name for a digital integrated circuit capable of being programmed to provide a variety of different logic functions In this chapter we will study: Combinational PLDs Sequential PLDs 32

33 Programmable Logic Devices Programmable Logic Arrays (PLA): A PLA performs the same basic function as a ROM. A PLA with n inputs and m outputs (Figure 9-28) can realize m functions of n variables. 33

34 Programmable Logic Devices 34

35 Programmable Logic Devices 35

36 Programmable Logic Devices PLA Tables: The symbols 0, l, and indicate whether a variable is complemented, not complemented, or not present in the corresponding product term. The output side of the table specifies which product terms appear in each output function. A 1 or 0 indicates whether a given product term is present or not present in the corresponding output function. 36

37 Programmable Logic Devices PLA Tables and ROM Truth Tables: In a ROM truth table each row represents a minterm; therefore, exactly one row will be selected by each combination of input values. The 0 s and 1 s of the output portion of the selected row determine the corresponding output values. On the other hand, each row in a PLA table represents a general product term. Therefore, zero, one, or more rows may be selected by each combination of input values. To determine the value of fi for a given input combination, the values of fi in the selected rows of the PLA table must be ORed together. 37

38 Programmable Logic Devices Programmable Array Logic (PAL): The PAL (programmable array logic) is a special case of the programmable logic array in which the AND array is programmable and the OR array is fixed PAL has same structure as PLA in Figure

39 Programmable Logic Devices 39

40 Programmable Logic Devices Implementing a Full Adder Using PAL: 40

41 Complex Programmable Logic Devices Complex Programmable Logic Devices (CPLD): Instead of a single PAL or PLA on a chip, many PALs or PLAs can be placed on a single CPLD chip and interconnected. 41

42 Complex Programmable Logic Devices Figure 9-35 shows how a signal generated in the PLA is routed to an I/O pin through a macrocell. 42

43 Field-Programmable Arrays Field-Programmable Gate Arrays (FPGA): An FPGA is an IC that contains an array of identical logic cells with programmable interconnections. The user can program the functions realized by each logic cell and the connections between the cells. The interior consists of an array of logic cells, also called configurable logic blocks (CLBs). The array of CLBs is surrounded by a ring of inputoutput interface blocks. These I/O blocks connect the CLB signals to IC pins. The space between the CLBs is used to route connections between the CLB outputs and inputs. 43

44 Field-Programmable Arrays FPGAs and CLBs: 44

45 Field-Programmable Arrays Implementing a Function Generator with Inputs a,b,c,d: The numbers in the squares represent the bits stored in the LUT. These bits enable particular minterms. Because the function being implemented is stored as a truth table, a function with only one minterm or with as many as 15 minterms requires a single function generator. 45

46 Field-Programmable Arrays Decomposition of Switching Functions: One method of decomposition is Shannon s Expansion Theorem. 46

47 Field-Programmable Arrays Realization of 5- and 6- Variable Functions: 47

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