Fungsi Kombinasi Logika
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…
Half-Adder
0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 Zero plus zero equals zero Zero plus one equals one One plus zero equals one One plus one equals zero with a carry of one Simple Binary Addition Program Studi T. Elektro FT - UHAMKA Slide - 7 3 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 Zero plus zero equals zero Zero plus one equals one One plus zero equals one One plus one equals zero with a carry of one
Basic Adder
Adder are important in computers and also in other types of digital systems in which numerical data are processed The half-adder accepts two binary digits on its inputs and produces two binary digits on its outputs, a sum bit and a carry bit Program Studi T. Elektro FT - UHAMKA Slide - 7 4 The half-adder accepts two binary digits on its inputs and produces two binary digits on its outputs, a sum bit and a carry bit
Half-Adder Logic
Cout AB A B Combinational Logic Program Studi T. Elektro FT - UHAMKA Slide - 7 5
The Full-Adder
The Full-Adder accepts two input bits and an input carry and generates a sum output and an output carry The basic different between a full-adder and a half-adder is that the full-adder accepts an input carry. Program Studi T. Elektro FT - UHAMKA Slide - 7 6 The basic different between a full-adder and a half-adder is that the full-adder accepts an input carry. The full-adder must add the two input bits and the input carry. From the half-adder, the sum of the input bits A and B is the exclusive-OR of those two variables. For the input carry (Cin) to be added to the input bits, it must be exclusive-ORed, and last yield the equation for the sum output of the full-adder Program Studi T. Elektro FT - UHAMKA Slide - 7 7 This is mean that to implement the full-adder sum function, two 2-input exclusive-OR gates can be used . The first must generate the term AB and the second has as its inputs the output of the first XOR gate and the input carry. The output carry is a 1 when both inputs to the first XOR gate are 1s or when both inputs to the second XOR gate are 1s. The output carry of full-adder is therefore produced by the inputs A ANDed with B and AB ANDed with Cin. Program Studi T. Elektro FT - UHAMKA Slide - 7 8 The output carry is a 1 when both inputs to the first XOR gate are 1s or when both inputs to the second XOR gate are 1s. The output carry of full-adder is therefore produced by the inputs A ANDed with B and AB ANDed with Cin. Full Adder from Two Half-Adder Circuits Program Studi T. Elektro FT - UHAMKA Slide - 7 9 Example: Determine the outputs for the inputs shown 1 0 0 1 0 1 Program Studi T. Elektro FT - UHAMKA Slide - 7 10 If A = 1, B = 1 and Cin = 1 ???? Σ = 0 Cout = 1
Parallel Binary Adder
A single full-adder is capable of adding two 1-bit numbers and an input carry. To add binary numbers with more than one 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. Elektro FT - UHAMKA Slide - 7 11 1 bit – 1FA 2 bit – 2FA 3 bit – 3FA 4 bit – 4FA ..and so on.. Example: Determine the sum generated by the 3-bit parallel adder 0 Program Studi T. Elektro FT - UHAMKA Slide - 7 12
Four-Bit Parallel Adders
4-Bits – Nibble Program Studi T. Elektro FT - UHAMKA Slide - 7 13 Truth Table for a 4-Bit Parallel Adder 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 truth table to find the sum and output carry for the following two 4-bit numbers if the input carry (Cn-1) is 0. A4A3A2A1 = 1100, B4B3B2B1 = 1100 Program Studi T. Elektro FT - UHAMKA Slide - 7 14 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 truth table to find the sum and output carry for the following two 4-bit numbers 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. Elektro FT - UHAMKA Slide - 7 15 Try This! 1011 add with 1010 and Assume Cn-1 = 0 10101 The 74LS283 4-Bit Parallel Adder Program Studi T. Elektro FT - UHAMKA Slide - 7 16
Adder Expansion
8-Bits 16-Bits Program Studi T. Elektro FT - UHAMKA Slide - 7 17 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. Elektro FT - UHAMKA Slide - 7 18 Σ8Σ7Σ6Σ5Σ4Σ3Σ2Σ1 = 101010111
Comparators
The basic function of a comparator is to compare the magnitude of two binary quantities to determine the relationship of those quantities 1-Bit Comparator 2-Bit Comparator 4-Bit Comparator Program Studi T. Elektro FT - UHAMKA Slide - 7 19 1-Bit Comparator 2-Bit Comparator 4-Bit Comparator 1-Bit Comparator The output is 1 when the inputs are equal 2-Bit Comparator Program Studi T. Elektro FT - UHAMKA Slide - 7 20 2-Bit Comparator The output is 1 when A0 = B0 AND A1 = B1 4-Bit Comparator One 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 bit position for an inequality Program Studi T. Elektro FT - UHAMKA Slide - 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 bit position for an inequality Example: Determine the A = B, A > B and A < B outputs for the input numbers shown on Figure below: A > B is HIGH and the other outputs are LOW Try This: A3A2A1A0 B3B2B1B0 1 0 0 1 1 0 1 0 Program Studi T. Elektro FT - UHAMKA Slide - 7 22 Try This: A3A2A1A0 B3B2B1B0 1 0 0 1 1 0 1 0 A < B is HIGH and the other 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. Elektro FT - UHAMKA Slide - 7 23 Binary decoder 4-bit decoder BCD-to-decimal decoder BCD-to-7-segement decoder Binary decoder The output is 1 only when: A0 = 1 A2 = 0 A3 = 0 A4 = 1 The output is only what we want! Program Studi T. Elektro FT - UHAMKA Slide - 7 24 Binary decoder The output is 1 only when: A0 = 1 A2 = 0 A3 = 0 A4 = 1 This is only one of an infinite number of examples Determine the logic required to decode the binary number 1011 by producing a HIGH level on the output X A3 A2A1A0 1011 Try This: Develop the logic required for 10010 and produce an active LOW output Program Studi T. Elektro FT - UHAMKA Slide - 7 25 X A3 A2A1A0 1011 Try This: Develop the logic required for 10010 and produce an active LOW output The 4-Bit Decoder In order to decode all possible combinations of 4-bits, sixteen gates are required (2 4 = 16). This type of decoder is commonly called either 4-line-to-16-line decoder or 1-of-16 decoder. Truth Table Program Studi T. Elektro FT - UHAMKA Slide - 7 26 Output is Active Low The 74HC154 1-of-16 Decoder The IC will active if gate output (EN) is HIGH If /CS1 and /CS2 are LOW, so EN will HIGH and IC is active! Program Studi T. Elektro FT - UHAMKA Slide - 7 27 If /CS1 and /CS2 are LOW, so EN will HIGH and IC is active! Example: A certain application requires that a 5-bit number be decoded. Use 74HC154 decoders to implement the logic. The binary number is represented by the format A4A3A2A1A0 . Determine the output in Figure that is activated for the binary input 1 0 1 1 0 ? Program Studi T. Elektro FT - UHAMKA Slide - 7 28 Determine the output in Figure that is activated for the binary input 1 0 1 1 0 ? Answer: 22 0 1 0 Enable Disable Disable Enable 1 The BCD-to-Decimal Decoder The BCD-to-decimal converts each BCD code into one of ten possible decimal digit indications. It is frequently referred as 4- line-to-10- line decoder or a 1-of-10 decoder. The method of implementation is the same as for the 1-of-16 decoder. Program Studi T. Elektro FT - UHAMKA Slide - 7 29 Example: The 74HC42 is an integrated circuit BCD-to-decimal decoder. The logic symbol is shown in Figure 1 below. If the input waveforms in Figure 2 are applied to the inputs of the 74HC42, show the output waveforms. 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 Program Studi T. Elektro FT - UHAMKA Slide - 7 30 Exercise: Construct a timing diagram showing input and output waveforms for the case where the BCD inputs sequence thru’ the decimal numbers as follows: 0, 2, 4, 6, 8, 1, 3, 5 and 9 Program Studi T. Elektro FT - UHAMKA Slide - 7 31 The BCD-to-7 Segment Decoder The BCD-to-7-segment decoder accepts the BCD code on its inputs and drive 7-segment display devices to produce a decimal readout. Program Studi T. Elektro FT - UHAMKA Slide - 7 32 Truth Table for BCD-to-7 Segment Decoder Program Studi T. Elektro FT - UHAMKA Slide - 7 33 Program Studi T. Elektro FT - UHAMKA Slide - 7 34
Encoders
Decimal-to-BCD encoder 8-line-to-3-line encoder Program Studi T. Elektro FT - UHAMKA Slide - 7 35 An encoder is a combinational logic circuit that essentially performs a “reverse” decoder function. The Decimal-to-BCD Encoder Program Studi T. Elektro FT - UHAMKA Slide - 7 36 1 3 5 7 9 2 3 6 7 4 5 6 7 8 9 0 1 2 3 A A A A The Decimal-to-BCD Encoder Program Studi T. Elektro FT - UHAMKA Slide - 7 37 1 3 5 7 9 2 3 6 7 4 5 6 7 8 9 0 1 2 3 A A A A 8-Line-to-3-Line Encoder Program Studi T. Elektro FT - UHAMKA Slide - 7 38 Multiplexer (Data Selectors) A multiplexer (MUX) is a device that allows digital information from several sources to be routed onto a single line for transmission over that line to a common destination. The basic multiplexer has several data-input lines and a single output line. It also has data-select inputs, which permit digital data on any one of the inputs to be switched to the output line. Program Studi T. Elektro FT - UHAMKA Slide - 7 39 A multiplexer (MUX) is a device that allows digital information from several sources to be routed onto a single line for transmission over that line to a common destination. The basic multiplexer has several data-input lines and a single output line. It also has data-select inputs, which permit digital data on any one of the inputs to be switched to the output line. 1-of-4 data MUX Program Studi T. Elektro FT - UHAMKA Slide - 7 40 3 1 0 2 1 0 1 1 0 0 1 0 Y D S S Y D S S Y D S S Y D S S Y D0 S1 S0 D1 S1S0 D2S1 S0 D3S1S0 Program Studi T. Elektro FT - UHAMKA Slide - 7 41 Y D0 S1 S0 D1 S1S0 D2S1 S0 D3S1S0 Example: Determine the output waveform in relation to the inputs Program Studi T. Elektro FT - UHAMKA Slide - 7 42 Exercise: Determine the output waveform in relation to the inputs Program Studi T. Elektro FT - UHAMKA Slide - 7 43 Multiplexer Larger multiplexers can be constructed from smaller ones. An 8-to-1 multiplexer can be constructed from smaller multiplexers as shown: Program Studi T. Elektro FT - UHAMKA Slide - 7 44 Multiplexer Application Example: Program Studi T. Elektro FT - UHAMKA Slide - 7 45 Demultiplexers A demultiplexer (DEMUX) basically reverses the multiplexing function. It takes digital information from one line and distributes it to a given number of output lines. Program Studi T. Elektro FT - UHAMKA Slide - 7 46 A demultiplexer (DEMUX) basically reverses the multiplexing function. It takes digital information from one line and distributes it to a given number of output lines. 3 1 0 2 1 0 1 1 0 0 1 0 D I S S D I S S D I S S D I S S 1-to-4 DEMUX Program Studi T. Elektro FT - UHAMKA Slide - 7 47 3 1 0 2 1 0 1 1 0 0 1 0 D I S S D I S S D I S S D I S S Example: Data Input = 1 and S1 and S0 = 1 D3 Exercise: Determine the data-output waveforms Program Studi T. Elektro FT - UHAMKA Slide - 7 48 1-to-8 DEMUX Program Studi T. Elektro FT - UHAMKA Slide - 7 49 1-line-to-8-line multiplexer Mux-Demux Application Example Program Studi T. Elektro FT - UHAMKA Slide - 7 50 This enables sharing a single communication line among a number of devices. At any time, only one source and one destination can use the communication line. Thank You “Hati seorang yang bodoh terletak di mulutnya, tetapi mulut seorang yang bijak terletak di hatinya” Program Studi T. Elektro FT - UHAMKA Slide - 7 51 “Hati seorang yang bodoh terletak di mulutnya, tetapi mulut seorang yang bijak terletak di hatinya”
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