CHAPTER 5COMBINATIONAL LOGIC

WITH MSI AND LSILEADER: CASTRO, JENADY GENE G.

MEMBERS:ALVARICO, MELLANIE R. RANAS, RENZO T.CAPISTRANO, KENNETH JOSHUA SECO, ERIC G.RAVILE, RNATO JR. ONGOSE, WILMAR A.SARMIENTO, ALEXANDRA U. LLONA, MYRNALYN D.

BSIT-1A

TOPICS Binary Parallel AdderMagnitude ComparatorEncoderDecoderMultiplexersProgrammable ROMsProgrammable 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

COMPARATOR

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<B.

An algorithm is a procedure that specifies a finite steps which if followed, gives the solution to a problem.

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-to-BCD-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 order input.

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

DECODERS

DECODERSo 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.

DECODERSo 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-to-decimal adder, because the identifying subscript of the high output line is always equal to the decimal value equivalent of the ABC input.

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 seven-segment 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-annode indicator.

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 0000.

MULTIPLEXERS

MULTIPLEXERSMultiplex 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.

• Figure 5.15 shows the logic diagram of a 74151 IC.

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.

PROGRAMMABLE ROMs

PROGRAMMABLE ROMs A programmable ROM (PROM) allows the

user, 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

74S472- 4096 bits organized as 512 X 8

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.

PROGRAMMABLE 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 minterms 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 possible input states.