Fungsi Kombinasi Logika · Use BCD-to-7-segment decoders in display ... 0 1 0 1 0 Use the 4-bit...

Fungsi KombinasiLogika

Program Studi T. ElektroFT - UHAMKA

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Endy Sjaiful AlimEndy Sjaiful AlimProgram Studi Teknik Elektro

Fakultas TeknikUniversitas Muhammadiyah Prof. Dr. HAMKA

Chapter Objectives

Distinguish between half-adder and full-adder Use BCD-to-7-segment decoders in display

systems Apply multiplexer in data selection Use decoders as multiplexer ….. and more…

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Distinguish between half-adder and full-adder Use BCD-to-7-segment decoders in display

systems Apply multiplexer in data selection Use decoders as multiplexer ….. and more…

Half-Adder

0 + 0 = 00 + 0 = 0

0 + 1 = 10 + 1 = 1

1 + 0 = 11 + 0 = 1

1 + 1 = 101 + 1 = 10

Zero plus zero equals zeroZero plus zero equals zero

Zero plus one equals oneZero plus one equals one

One plus zero equals oneOne plus zero equals one

One plus one equals zero with a carryOne plus one equals zero with a carryof oneof one

Simple Binary Addition

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0 + 0 = 00 + 0 = 0

0 + 1 = 10 + 1 = 1

1 + 0 = 11 + 0 = 1

1 + 1 = 101 + 1 = 10

Zero plus zero equals zeroZero plus zero equals zero

Zero plus one equals oneZero plus one equals one

One plus zero equals oneOne plus zero equals one

One plus one equals zero with a carryOne plus one equals zero with a carryof oneof one

Basic AdderAdder are important in computers and also in other types ofdigital systems in which numerical data are processed

The half-adder accepts two binary digitson its inputs and produces two binarydigits on its outputs, a sum bit and a carrybit

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The half-adder accepts two binary digitson its inputs and produces two binarydigits on its outputs, a sum bit and a carrybit

Half-Adder Logic

ABCout BA Combinational Logic

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The Full-AdderThe Full-Adder accepts two input bits andan input carry and generates a sumoutput and an output carry

The basic different between a full-adder and a half-adderis that the full-adder accepts an input carry.

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The basic different between a full-adder and a half-adderis that the full-adder accepts an input carry.

The full-adder must add the two input bits and the inputcarry. From the half-adder, the sum of the input bits A andB is the exclusive-OR of those two variables. For the inputcarry (Cin) to be added to the input bits, it must beexclusive-ORed, and last yield the equation for the sumoutput of the full-adder

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This is mean that to implement the full-adder sum function,two 2-input exclusive-OR gates can be used . The first mustgenerate the term AB and the second has as its inputsthe output of the first XOR gate and the input carry.

The output carry is a 1 when both inputs to the first XORgate are 1s or when both inputs to the second XOR gateare 1s. The output carry of full-adder is therefore producedby the inputs A ANDed with B and AB ANDed with Cin.

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The output carry is a 1 when both inputs to the first XORgate are 1s or when both inputs to the second XOR gateare 1s. The output carry of full-adder is therefore producedby the inputs A ANDed with B and AB ANDed with Cin.

Full Adder from Two Half-AdderCircuits

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Example: Determine the outputsfor the inputs shown

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If A = 1, B = 1 and Cin = 1 ????

Σ = 0

Cout = 1

Parallel Binary AdderA single full-adder is capable of adding two 1-bit numbersand an input carry. To add binary numbers with more thanone bit, we must use additional full-adders.

1 bit – 1FA

2 bit – 2FA

3 bit – 3FA

4 bit – 4FA

..and so on..

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1 bit – 1FA

2 bit – 2FA

3 bit – 3FA

4 bit – 4FA

..and so on..

Example: Determine the sum generated by the 3-bitparallel adder

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Four-Bit Parallel Adders4-Bits – Nibble

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Truth Table for a 4-Bit ParallelAdder

Cn-1 An Bn Σn Cn

0 0 0 0 0

0 0 1 1 0

0 1 0 1 0 Use the 4-bit parallel adder truthtable to find the sum and outputcarry for the following two 4-bitnumbers if the input carry (Cn-1) is 0.

A4A3A2A1 = 1100, B4B3B2B1 = 1100

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0 1 0 1 0

0 1 1 0 1

1 0 0 1 0

1 0 1 0 1

1 1 0 0 1

1 1 1 1 1

Use the 4-bit parallel adder truthtable to find the sum and outputcarry for the following two 4-bitnumbers if the input carry (Cn-1) is 0.

A4A3A2A1 = 1100, B4B3B2B1 = 1100

n=1, A1 = 0, B1 = 0 and Cn-1 = 0

n=2, A2 = 0, B2 = 0 and Cn-1 = 0

n=3, A3 = 1, B3 = 1 and Cn-1 = 0

n=4, A4 = 1, B4 = 1 and Cn-1 = 1

Σ1 = 0 and C1 = 0

Σ2 = 0 and C2 = 0

Σ3 = 0 and C3 = 1

Σ4 = 1 and C4 = 1

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Try This!

1011 add with1010 andAssume Cn-1 = 0

The 74LS2834-Bit Parallel

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Adder Expansion

8-Bits

16-Bits

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16-Bits

Example:Show how two 74LS283 adders can be connected to form an 8-bit parallel adder.Show output bits for the following 8-bit input numbers:A8A7A6A5A4A3A2A1 = 10111001 and B8B7B6B5B4B3B2B1 = 10011110

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Σ8Σ7Σ6Σ5Σ4Σ3Σ2Σ1 = 101010111

ComparatorsThe basic function of a comparator is to compare themagnitude of two binary quantities to determine therelationship of those quantities

1-Bit Comparator 2-Bit Comparator 4-Bit Comparator

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1-Bit Comparator 2-Bit Comparator 4-Bit Comparator

1-Bit Comparator

The output is 1 when the inputs are equalThe output is 1 when the inputs are equal

2-Bit Comparator

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2-Bit Comparator

The output is 1 when AThe output is 1 when A00 = B= B00 AND AAND A11 = B= B11

4-Bit ComparatorOne of three outputs will be HIGH: A greater than B (A > B) A equal to B (A = B) A less than B (A < B)

To determine an inequality of binary numbers A and B,first

the highest order bit in each number. The following

conditions are possible:

1. If A3 = 1 and B3 = 0, number A is greater than number B

2. If A3 = 0 and B3 = 1, number A is less than number B

3. If A3 = B3 then you must examine the next lower bitposition for an inequalityProgram Studi T. Elektro

FT - UHAMKASlide - 7 21

To determine an inequality of binary numbers A and B,first

the highest order bit in each number. The following

conditions are possible:

1. If A3 = 1 and B3 = 0, number A is greater than number B

2. If A3 = 0 and B3 = 1, number A is less than number B

3. If A3 = B3 then you must examine the next lower bitposition for an inequality

Example:Determine the A = B, A > B and A < B outputs for the inputnumbers shown on Figure below:

A > B is HIGH and theother outputs are LOW

Try This:

A3A2A1A0 B3B2B1B0

1 0 0 1 1 0 1 0

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Try This:

A3A2A1A0 B3B2B1B0

1 0 0 1 1 0 1 0A < B is HIGH and theother outputs are LOW

Try This:

A3A2A1A0 B3B2B1B0

1 0 1 1 1 0 1 0

Decoders

Binary decoder 4-bit decoder BCD-to-decimal decoder BCD-to-7-segement decoder

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Binary decoder 4-bit decoder BCD-to-decimal decoder BCD-to-7-segement decoder

Binary decoderThe output is 1 only when:

A0 = 1A2 = 0A3 = 0A4 = 1

The output isonly what wewant!

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Binary decoderThe output is 1 only when:

A0 = 1A2 = 0A3 = 0A4 = 1

This is only one of an infiniteThis is only one of an infinitenumber of examplesnumber of examples

Determine the logic required to decode the binary number 1011 byproducing a HIGH level on the output

10110123 AAAAX

Try This:

Develop the logicrequired for 10010and produce anactive LOW output

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10110123 AAAAX

Try This:

Develop the logicrequired for 10010and produce anactive LOW output

The 4-Bit DecoderIn order to decode all possible combinations of 4-bits, sixteengates are required (24 = 16). This type of decoder is commonlycalled either 4-line-to-16-line decoder or 1-of-16 decoder.

TruthTable

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Output isActiveLow

The 74HC154 1-of-16 DecoderThe IC will active ifgate output (EN) isHIGH

If /CS1 and /CS2 areLOW, so EN will HIGHand IC is active!

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If /CS1 and /CS2 areLOW, so EN will HIGHand IC is active!

Example:A certain application requires that a 5-bit number be decoded. Use 74HC154decoders to implement the logic. The binary number is represented by the formatA4A3A2A1A0.

Determine theoutput in Figurethat isactivated forthe binary input1 0 1 1 0 ?

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Determine theoutput in Figurethat isactivated forthe binary input1 0 1 1 0 ?

Answer:

Enable DisableEnableDisable

The BCD-to-Decimal DecoderThe BCD-to-decimal converts each BCD code into one of tenpossible decimal digit indications. It is frequently referred as 4-line-to-10- line decoder or a 1-of-10 decoder. The method ofimplementation is the same as for the 1-of-16 decoder.

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Example:The 74HC42 is an integrated circuit BCD-to-decimal decoder. The logic symbol isshown in Figure 1 below. If the input waveforms in Figure 2 are applied to theinputs of the 74HC42, show the output waveforms.

0 1 0 1 0 1 0 1 0 10 0 1 1 0 0 1 1 0 0

0 0 0 0 1 1 1 1 0 00 0 0 0 0 0 0 0 1 1

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Exercise:Construct a timing diagram showing input and output waveforms forthe case where the BCD inputs sequence thru’ the decimal numbers asfollows: 0, 2, 4, 6, 8, 1, 3, 5 and 9

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The BCD-to-7 Segment DecoderThe BCD-to-7-segment decoder accepts the BCD code onits inputs and drive 7-segment display devices to producea decimal readout.

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Truth Table for BCD-to-7 SegmentDecoder

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Encoders

Decimal-to-BCD encoder 8-line-to-3-line encoder

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An encoder is a combinational logic circuit thatessentially performs a “reverse” decoder function.

The Decimal-to-BCD Encoder

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AThe Decimal-to-BCD Encoder

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8-Line-to-3-Line Encoder

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Multiplexer (Data Selectors) A multiplexer (MUX) is a device that allows digital

information from several sources to be routed onto asingle line for transmission over that line to acommon destination.

The basic multiplexer has several data-input linesand a single output line.

It also has data-select inputs, which permit digitaldata on any one of the inputs to be switched to theoutput line.

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A multiplexer (MUX) is a device that allows digitalinformation from several sources to be routed onto asingle line for transmission over that line to acommon destination.

The basic multiplexer has several data-input linesand a single output line.

It also has data-select inputs, which permit digitaldata on any one of the inputs to be switched to theoutput line.

1-of-4 data MUX

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013012011010 SSDSSDSSDSSDY

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013012011010 SSDSSDSSDSSDY

Example:Determine the output waveform in relation to the inputs

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Exercise: Determine the output waveform in relation tothe inputs

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Multiplexer Larger multiplexers can be constructed from smaller ones.

An 8-to-1 multiplexer can be constructed from smallermultiplexers as shown:

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MultiplexerApplication Example:

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Demultiplexers

A demultiplexer (DEMUX) basically reversesthe multiplexing function.

It takes digital information from one line anddistributes it to a given number of outputlines.

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A demultiplexer (DEMUX) basically reversesthe multiplexing function.

It takes digital information from one line anddistributes it to a given number of outputlines.

1-to-4 DEMUX

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Example: Data Input = 1 and S1 and S0 = 1 D3

Exercise:Determine the data-output waveforms

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1-to-8 DEMUX

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1-line-to-8-line multiplexer

Mux-Demux Application Example

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This enables sharing a single communication line among anumber of devices.At any time, only one source and one destination can use thecommunication line.

Thank You

“Hati seorang yang bodohterletak di mulutnya, tetapi mulut

seorang yang bijak terletak dihatinya”

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“Hati seorang yang bodohterletak di mulutnya, tetapi mulut

seorang yang bijak terletak dihatinya”

Fungsi Kombinasi Logika · Use BCD-to-7-segment decoders in display ... 0 1 0 1 0 Use the 4-bit...

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