fungsi kombinasi logika · use bcd-to-7-segment decoders in display ... 0 1 0 1 0 use the 4-bit...
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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…
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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.
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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.
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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Example: Determine the outputsfor the inputs shown
1
0
0
1
0
1
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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..
Program Studi T. ElektroFT - UHAMKA
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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
0
Program Studi T. ElektroFT - UHAMKA
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Four-Bit Parallel Adders4-Bits – Nibble
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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
11000
Program Studi T. ElektroFT - UHAMKA
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Try This!
1011 add with1010 andAssume Cn-1 = 0
10101
The 74LS2834-Bit Parallel
Adder
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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
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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!
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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!
Program Studi T. ElektroFT - UHAMKA
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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 ?
Program Studi T. ElektroFT - UHAMKA
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Determine theoutput in Figurethat isactivated forthe binary input1 0 1 1 0 ?
Answer:
22
0
10
Enable DisableEnableDisable
1
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.
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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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.
Program Studi T. ElektroFT - UHAMKA
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Truth Table for BCD-to-7 SegmentDecoder
Program Studi T. ElektroFT - UHAMKA
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Program Studi T. ElektroFT - UHAMKA
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Encoders
Decimal-to-BCD encoder 8-line-to-3-line encoder
Program Studi T. ElektroFT - UHAMKA
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An encoder is a combinational logic circuit thatessentially performs a “reverse” decoder function.
The Decimal-to-BCD Encoder
Program Studi T. ElektroFT - UHAMKA
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97531
7632
7654
98
0
1
2
3
A
A
A
AThe Decimal-to-BCD Encoder
Program Studi T. ElektroFT - UHAMKA
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97531
7632
7654
98
0
1
2
3
A
A
A
A
8-Line-to-3-Line Encoder
Program Studi T. ElektroFT - UHAMKA
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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.
Program Studi T. ElektroFT - UHAMKA
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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
Program Studi T. ElektroFT - UHAMKA
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013
012
011
010
SSDY
SSDY
SSDY
SSDY
013012011010 SSDSSDSSDSSDY
Program Studi T. ElektroFT - UHAMKA
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013012011010 SSDSSDSSDSSDY
Example:Determine the output waveform in relation to the inputs
Program Studi T. ElektroFT - UHAMKA
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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:
Program Studi T. ElektroFT - UHAMKA
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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.
Program Studi T. ElektroFT - UHAMKA
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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.
013
012
011
010
SSID
SSID
SSID
SSID
1-to-4 DEMUX
Program Studi T. ElektroFT - UHAMKA
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013
012
011
010
SSID
SSID
SSID
SSID
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”
Program Studi T. ElektroFT - UHAMKA
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“Hati seorang yang bodohterletak di mulutnya, tetapi mulut
seorang yang bijak terletak dihatinya”
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