Tugas 8. Rangkuman Fungsi Kombinasi Logika
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
Simple Binary Addition
0 + 0 = 0 Zero plus zero equals zero
0 + 1 = 1 Zero plus one equals one
1 + 0 = 1 One plus zero equals one
1 + 1 = 10 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.
Definition : 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
The Full-Adder
Definition : 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.
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.
Full Adder from Two Half-Adder Circuits
Example: Determine the outputs for the inputs shown
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.
Example: Determine the sum generated by the 3-bit parallel adder
Four-Bit Parallel Adders
4-Bits – Nibble
Truth Table for a 4-Bit Parallel Adder
Example : 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
Solution :
Adder Expansion
Comparators
The basic function of a comparator is to compare the magnitude of two binary quantities to determine the relationship of those quantities.
The output is 1 when A0 = B0 AND A1 = B1
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.
Decoders
· 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!
· 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.
· 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.
· 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.
Encoders
· Decimal-to-BCD encoder
· 8-line-to-3-line encoder
An encoder is a combinational logic circuit that essentially performs a “reverse” decoder function.
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.
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.
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