Lecture 18: Digital Logic Design PDF

CS302 – Digital Logic Design a) 2-Input 4-Bit Multiplexer The MSI, 74X157 is a 2-input, 4-bit Multiplexer. This multiplexer has two sets of 4-bit inputs. It also has 4-bit outputs. The single select input line allows the first set of four inputs or the second set of 4-inputs to be connected...

CS302 – Digital Logic Design a) 2-Input 4-Bit Multiplexer The MSI, 74X157 is a 2-input, 4-bit Multiplexer. This multiplexer has two sets of 4-bit inputs. It also has 4-bit outputs. The single select input line allows the first set of four inputs or the second set of 4-inputs to be connected to the output. Thus four-bits of data from two sources are routed to the output. The function table and the circuit of the multiplexer are shown. table 18.1, figure 18.1 The multiplexer has two sets of 4-bit active-high inputs 1A, 2A, 3A, 4A and 1B, 2B, 3B, 4B respectively. The multiplexer has 4-bit active-high outputs 1Y, 2Y, 3Y 4Y. The single select input allows either the 4-bit input A or the 4-bit input B to be connected to the 4-bit output Y. The G active-low pin enables or disables the Multiplexer. Inputs Outputs G S 1Y 2Y 3Y 4Y 1 X 0 0 0 0 0 0 1A 2A 3A 4A 0 1 1B 2B 3B 4B Table 18.1 Function table of 2-Input 4-Bit Multiplexer Figure 18.1 2-input 4-bit Multiplexer Virtual University of Pakistan Page 184 CS302 – Digital Logic Design Expanding Multiplexers Multiplexers have to be connected together to form larger multiplexer to fulfil specific application requirements. 1. 8-Input Multiplexer A single dual, 4-input multiplexer 74X153 can be connected to form an 8-input multiplexer. The circuit diagram and the function table are shown in fig. 18.2 and table 18.2 respectively. The two active-low enable inputs of the two 4-input multiplexers are connected together using a NOT gate to form the C input of the 8-input multiplexer. When C is set to 0, the first multiplexer is selected allowing its inputs 1C0, 1C1, 1C2 and 1C3 to be selected through select inputs A and B. When C is set to 1, the second multiplexer is selected allowing its inputs and outputs to be used. The two outputs are connected through an OR gate. Figure 18.2 8-to-1 Multiplexer using two 4-to-1 Multiplexers Input Output C B A F 0 0 0 1C0 0 0 1 1C1 0 1 0 1C2 0 1 1 1C3 1 0 0 2C0 1 0 1 2C1 1 1 0 2C2 1 1 1 2C3 Table 18.2 Function Table of a 8-to-1 Multiplexer Virtual University of Pakistan Page 185 CS302 – Digital Logic Design 2. 16-Input Multiplexer Two 74XX153 Dual, 4-input multiplexer can be connected to form a 16-input multiplexer. The circuit diagram and the function table of the 16 input multiplexer are shown in Figure 18.3 and table 18.3 respectively. The select inputs A and B of the two dual, 4-input multiplexers are connected together which allows selection of any one input out of the four set of 4-bit inputs. The four active-low multiplexer enable inputs which allow selection of any one of the four multiplexers are connected to the active-low outputs of a 2-to-4 decoder. The decoder inputs C and D enable one out of the four multiplexers. The four outputs are connected together through a 4-input OR gate. The G enable input of the decoder when set to 1 disables the decoder and the multiplexers. Figure 18.3 16-input Multiplexer 3. 2-Input, 8-bit Multiplexer Two 2-input, 4-bit multiplexers 74X157 can be connected to implement a 2-input, 8-bit multiplexer. The circuit diagram is shown in figure 18.4. The select S inputs of the two multiplexers are connected together so that the 4-bit inputs A of both the multiplexers are selected simultaneously when S is set to logic low. Similarly, by setting the S input to logic-high the B inputs of both the multiplexers are selected. The active- low enable inputs G of both the multiplexers are also connected together so that both the Virtual University of Pakistan Page 186 CS302 – Digital Logic Design multiplexers are enabled and disabled simultaneously by setting the G input to 0 or 1 respectively. Inputs Output G D C B A F 1 x x x x 0 0 0 0 0 0 1C0 (M1) 0 0 0 0 1 1C1 (M1) 0 0 0 1 0 1C2 (M1) 0 0 0 1 1 1C3 (M1) 0 0 1 0 0 2C0 (M1) 0 0 1 0 1 2C1 (M1) 0 0 1 1 0 2C2 (M1) 0 0 1 1 1 2C3 (M1) 0 1 0 0 0 1C0 (M2) 0 1 0 0 1 1C1 (M2) 0 1 0 1 0 1C2 (M2) 0 1 0 1 1 1C3 (M2) 0 1 1 0 0 2C0 (M2) 0 1 1 0 1 2C1 (M2) 0 1 1 1 0 2C2 (M2) 0 1 1 1 1 2C3 (M2) Table 18.3 Function Table of 16-bit Multiplex Figure 18.4 2-Input, 8-bit Multiplexer Virtual University of Pakistan Page 187 CS302 – Digital Logic Design Applications of Multiplexers Multiplexers are used in a wide variety of applications. Their primary use is to route data from multiple sources to a single destination. Other than its use as a Data router, a parallel to serial converter, logic function generator and used for operation sequencing. 1. Data Routing A two digit 7-Segment display uses two 7-Segments Display digits connected to two BCD to 7-Segment display circuits. To display the number 29 the BCD number 0010 representing the MSD is applied at the inputs of the BCD to 7-Segment display circuit connected to the MSD 7-Segment Display Digit. Similarly, the BCD input 1001 representing the numbers 9 is applied at the inputs of the LSD display circuit. The circuit uses two BCD to 7-Segment decoder circuits to decode each of the two BCD inputs to the respective 7-Segment display outputs. Figure 18.5. The display circuit can be implemented using a single BCD to 7-Segment IC and a Multiplexer. Figure 18.5 2-Digit Decimal Display Circuit To fully understand the working of the alternate circuit it is essential to understand the working of the 7-Segment Display Digit. 7-Segment Display Digits are implemented using 7 LEDs (Light Emitting Diodes) connected in the form of number 8. To turn on a LED, its Anode is connected to +5 volts and its Cathode is connected to Virtual University of Pakistan Page 188 CS302 – Digital Logic Design Ground or 0 volts. 7-Segment displays are of two types, the Common Anode type and the Common Cathode type. a. Common Anode 7-Segment Display The Common Anode 7-Segment Display has positive end of each of the seven display segments (LEDs) connected together. To display any segment the Common Anode of the display has to be connected to +5 volts and the other end of each segment has to be connected to 0 volts. Figure 18.6a b. Common Cathode 7-Segment Display The Common Cathode 7-Segment Display has negative end of each of the seven display segments (LEDs) connected together. To display any segment the Common Cathode of the display has to be connected to 0 volts and the other end of each segment has to be connected to +5 volts. Figure 18.6b. Figure 18.6 Common Anode and Common Cathode 7-Segment Displays The alternate 2-digit display circuit based on a multiplexer and a BCD to 7- Segment Decoder is shown in figure 18.7. The BCD numbers of the two digits to be displayed are applied at the inputs A and B of the multiplexer. The 4-bit output of the Multiplexer is connected to the 4-bit input of the BCD to 7-Segment Decoder circuit. The 7-Segment output of the Decoder is connected to the 7 segments of both the Common Cathode Displays. The MSD/LSD input is connected to the select input of the Multiplexer, the Common Cathode of the MSD and the Common Cathode of the LSD through a NOT gate. The MSD is applied at Input A, and the LSD at input B. To Display the MSD the MSD/LSD input is set to 0. The BCD number at Input A of the multiplexer is selected and routed through the BCD to 7-Segment Decoder to both the two 7-Segment Displays. Since the MSD/LSD input is 0 therefore the MSD display is selected and the MSD is displayed. The MSD/LSD input is switched to 1, which selects the BCD at input B which is routed through the Multiplexer to the 7-Segment Decoder and ultimately to the 7-segment displays. Since the MSD/LSD is set to 1, the Common Cathode of the LSD is connected to zero, thus the number at input B of the multiplexer is displayed on the LSD display. The MSD/LSD input is rapidly switched between 0 and 1 to allow both the Virtual University of Pakistan Page 189 CS302 – Digital Logic Design digits to be seen on the 2-digit display. This circuit can be expanded to incorporate any number of digits. Figure 18.7 2-Digit Decimal Display using a Multiplexer 2. Parallel to Series Conversion In a Digital System, Binary data is used and represented in parallel. Parallel data is a set of multiple bits. For example, a nibble is a parallel set of 4-bits, a byte is a parallel set of 8 bits. When two binary numbers are added, the two numbers are represented in parallel and the parallel adder works and generates a sum term which is also in parallel. Transmission of information to remote locations through a piece of wire requires that the parallel information (data) be converted into serial form. In a serial data representation, data is represented by a sequence of single bits. An 8-bit parallel data can be transmitted through a single piece of wire 1-bit at a time. Transmitting 8-bits simultaneously (in parallel form) requires 8 separate wires for the 8-bits. Laying of 8 wires across two remote locations for data transfer is expensive and is therefore not practical. All communication systems set up across remote locations use serial transmission. An 8-bit parallel data can be converted into serial data by using an 8-to-1 multiplexer such as 74X151 which has 8 inputs and a single output. The 8-bit data which is to be transmitted serially is applied at the 8 inputs I0-7 of the multiplexer. A three bit counter which counts from 0 to 7 is connected to the three select inputs S0, S1 and S2. The counter is connected to a clock which sends a clock pulse to the counter every 1 millisecond. Initially, the counter is reset to 000, the I0 input is selected and the data at input I0 is routed to the output of the multiplexer. On receiving the clock signal after 1 Virtual University of Pakistan Page 190 CS302 – Digital Logic Design millisecond the counter increments its count from 000 to 001 which selects I1 input of the multiplexer and routes the data present at the input to the output. Similarly, at the next clock pulse the counter increments to 010, selecting I2 input and routing the data to the output. Thus after 8 milliseconds the parallel data is routed to the output 1-bit at a time. The output of the multiplexer is connected to the wire through which the serial data is transmitted. Figure 18.8 Figure 18.8a Parallel to Serial Conversion 0 1 2 3 4 5 6 7 C0 C1 C2 Y Figure 18.8b Timing diagram of the Parallel to Serial Conversion Circuit Virtual University of Pakistan Page 191 CS302 – Digital Logic Design 3. Logic Function Generator Multiplexers can be used to implement a logic function directly from the function table without the need for simplification. The select inputs of the multiplexer are used as the function variables. The inputs of the multiplexer are connected to logic 1 and 0 to represent the missing and available terms. The three variable function table and its 8-to-1 multiplexer based function implementation is shown in figure 18.9 Input Output A B C Y 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 Figure 18.9 Logic Function Generator based on 3-variable logic function table 4. Operation Sequencing Many industrial applications have processes that run in a sequence. A paint manufacturing plant might have a four step process to manufacture paint. Each of the four steps runs in a sequence one after the other. The second step can not start before the first step has completed. Similarly, the third and fourth step of the paint manufacturing process can not proceed unless steps two and three have completed. It is not necessary that each of the manufacturing steps is of the same duration. Each manufacturing step can have different time duration and can be variable depending upon the quantity of paint manufactured or other parameters. Normally, the end of each step in the manufacturing process is indicated by a signal which is actuated by some machine which has completed its part of the manufacturing process. On receiving the signal the next step of the manufacturing process is initiated. The entire sequence of operations is controlled by a Multiplexer and a Decoder circuit. Figure 18.10. The manufacturing processes are started by resetting the 2-bit counter to 00. The counter output is connected to the select input of the Multiplexer and the inputs of the Decoder which selects the Multiplexer input I0 is and activates the Decoder output Y0. The Decoder output is connected to initiate the first process. When the process completes it indicates the completion of the process by setting its output to logic 1. The output of Process 1 is connected to I0 input of the Multiplexer. When Process 1 sets its output to 1 to indicate its completion, the logic 1 is routed by the Multiplexer to the clock input of the 2-it counter. The counter on receiving logic 1 increments its count to 01, which selects I1 input of the Multiplexer and the Y1 output of Virtual University of Pakistan Page 192 CS302 – Digital Logic Design the Decoder. The input to Process 1 is deactivated and Process 2 is activated by Y1. On completion of Process 2 its output is set to logic 1, which is routed by the multiplexer to the clock input of the 2-bit counter which increments to the next count. This continues until Process 4 signals its completion after which the Decoder and the Multiplexer is deselected completing the manufacturing process. Figure 18.10 Control of Manufacturing process through Operation Sequencing Virtual University of Pakistan Page 193