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CHAPTER 5 COMBINATIONAL LOGIC WITH MSI AND LSI LEADER: CASTRO, JENADY GENE G. : ALVARICO, MELLANIE R. RANAS, RENZO T. CAPISTRANO, KENNETH JOSHUA SECO, ERIC G. RAVILE, RNATO JR. ONGOSE, WILMAR A. SARMIENTO, ALEXANDRA U. LLONA,

TOPICS  Binary Parallel Adder Magnitude Comparator Encoder Decoder Multiplexers Programmable ROMs Programmable Array

BINARY PARALLEL ADDER

BINARY PARALLEL ADDER  A Binary Parallel Adder is a digital function that produces the arithmetic function sum of two binary numbers in parallel.  It consists of full-ladders connected in cascade, with the output carry from one full-ladder connected to the input carry of the next full ladder.

BINARY PARALLEL ADDER  Figure 5.1 shows the interconnection of four full-adder (FA) circuits to provide a 4-bit binary parallel adder.  The addend bits of A and the addend bits of B are designated by subscript numbers from right to left with subscript 1 denoting the low-order bit.

FIGURE 5.1. 4-BIT FULL ADDER

DECIMAL ADDER  A Decimal Adder requires a minimum of nine inputs and five outputs, since four bits are required to code each decimal digit and the circuit must have an input carry and output carry.

BCD ADDER  A BCD Adder is a circuit that adds two BCD digits in parallel and produces a sum digit also in BCD.

FIGURE 5.2 BLOCK DIAGRAM OF A BCD ADDER

MAGNITUDE COMPARATO R

MAGNITUDE COMPARATOR  A Magnitude Comparator is a combinational circuit that compares two numbers, A and B, and determines their relative magnitudes.  The outcome of the comparison is specified by three binary variables that indicate whether A>B, A=B or A
FIGURE 5.3 FOUR-BIT MAGNITUDE COMPARATOR

ENCODER

ENCODER • An encoder converts an active input signal into a coded output signal. • There are n input lines, only one of which is active. • Internal logic within the encoder converts this active input into a coded binary output with m bits.

ENCODER • The type of encoder available in IC form is called a priority encoder. • A priority encoder monitor several lines and assigns each of them a priority. • If one of the lines is activated, the priority encoder produces an output indicating which line it is.

DECIMAL-TO-BCD-ENCODER • A common type of encoder is the decimal-toBCD-encoder which is illustrated in Figure 5.4 • The switches are push-button switches like those of a pocket calculator. • When button 3 is pressed, the C and D OR gates have high inputs; therefore, the output is: ABCD= 0011 • If button 6 is pressed, the output becomes: ABCD= 0110.

FIGURE 5.4 DECIMAL-TO-BCD ENCODER

DECIMAL-TO-BCD-ENCODER • Figure 5.5 (a) shows the pin configuration for a 74147 and (b) shows how to represent a 74147 by means of a schematic diagram. • The bubbles indicate active-low inputs and outputs. • The 74147 is called a priority encoder because it gives priority to the highest

FIGURE 5.5 (a) PINOUT DIAGRAM OF 74147 (b) LOGIC DIAGRAM

DECODERS

DECODERS o A digital decoder has 2N outputs and accepts N inputs. o Only the output that corresponds to the binary number on the input lines is activated. o Decoders are used in many digital circuits. o They can be used to select memory addresses, and to decode instructions in a computer. o They are used whenever only one line from several possible lines must be selected.

DECODERS o A decoder is similar to a demultiplexer, with one exception- there is no data input. o The only inputs are the control bits ABC, which are illustrated in Figure 5.6. o The logic circuit is called a 1-of-8 decoder because only 1 of the 8 output lines can be high. o Sometimes the circuit is called a binary-todecimal adder, because the identifying subscript of the high output line is always equal to the decimal value equivalent of the

SEVEN-SEGMENT DECODERS  A light-emitting diode (LED) emits radiation when forward biased because the LED’s free electrons recombine with holes near the junction.  A diode is said to be in a forward bias condition when it the diode have a nominal voltage of 0.7 V across its terminal when conducting current.  Figure 5.7 shows a seven-segment indicator with seven LEDs labeled a through g.

SEVEN-SEGMENT DECODERS  Seven-segment indicators may be of the common-cathode type in which all annodes are connected together.  A seven-segment decoder-driver is an IC decoder that can be used to drive a sevensegment indicator.  There are two types of decoder drivers; one for common-annode indicators and the other for common-cathode indicators.  Figure 5.9 shows a 7446 driving a common-

DECIMAL TO SEVEN-SEGMENT CONNECTION Figure 5.10 shows the block diagram for displaying the 10 digits of the decimal number system. It consists of ten switches which corresponds to count 0 to count 9. This circuit functions in a way that, when a particular switch is on, for instance if the switch for count 0 is turned on, the decimal to BCD circuitry will convert this to its corresponding binary equivalent which is

MULTIPLEXE RS

MULTIPLEXERS Multiplex means many into one. A multiplexer is a circuit with many inputs but only one output.  The inputs to a multiplexer are represented by the several input lines shown. One of the input lines is connected to the output. The basic multiplexer operation is shown in Figure 5.13.

THE 74151 MULTIPLEXERS • Multiplexers can be constructed out of AND and OR gates, but there is no need to do so. • Several multiplexers exist in the 7400 family. • One of these is the 74151 the pinout program of which is given in Figure 5.14 • It is an 8-to-1 multiplexer in a 16-pin package.

NIBBLE MULTIPLEXERS • When a binary number has 4 bits, it is called a nibble. • Sometimes we want to select one of two input nibbles. • In this case, we can use a nibble multiplexer like the one shown in Figure 5.16.

DEMULTIPLEXER • Demultiplex means one into many. • A demultiplex is a logic circuit with one input and many outputs. • By applying control signals, we can direct the input signal to one of the output lines. • The demultiplexing principle is illustrated in Figure 5.17, where it was assumed that only one switch is closed at any one time.

PROGRAMMABL E ROMs

PROGRAMMABLE ROMs  A programmable ROM (PROM) allows the , instead of the manufacturer, to store the data.  An instrument called a PROM programmer stores the words by “burning in”.  Here are some commercially available PROMs: 74S188- 256 bits organized as 32 X 8 74S287- 1024 bits organized as 256 X 4

SIMPLIFIED DRAWING OF A PROM • An alternate, streamlined drawing procedure for PROMs like the one in Figure 5.20 is shown in Figure 5.21. • In this simplified drawing, the solid black bullets indicated connections to the AND gates inputs. • Each bullet represents a fixed connection that cannot be changed.

PROGRAMMING A PROM • Generating a Boolean function at the output of a PROM is accomplished by fusing (melting) fusible links along the inputs to the OR gates in Figure 5.21.

PROGRAMMABL E LOGIC ARRAY

PROGRAMMABLE LOGIC ARRAY  A Programmable Logic Array or PLA is similar to a ROM in concept.  The difference, however, is that the PLA does not provide full decoding of the variables and does not generate all the min as in the ROM.  A PLA having 3 input variables (ABC) and 3 output variables (XYZ) is illustrated in Figure 5.22  Eight AND gates are required to decode the 8