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# Thế giới ASIC

## Digital Combinational Logic Part-V

Multiplexer
A multiplexer (MUX) is a digital switch which connects data from one of n sources to the output. A number of select inputs determine which data source is connected to the output. The block diagram of MUX with n data sources of b bits wide and s bits wide select line is shown in below figure.

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## Digital Combinational Logic Part-IV

Encoders
An encoder is a combinational circuit that performs the inverse operation of a decoder. If a device output code has fewer bits than the input code has, the device is usually called an encoder. e.g. 2n-to-n, priority encoders.

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## Digital Combinational Logic Part-III

Decoders
A decoder is a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs, where the input and output codes are different; e.g. n-to-2n, BCD decoders

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## Digital Logic Families Part-II

Noise Margin

Gate circuits are constructed to sustain variations in input and output voltage levels. Variations are usually the result of several different factors.
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## Digital Logic Families part I

Digital Logic Families
Logic families can be classified broadly according to the technologies they are built with. In earlier days we had vast number of these technologies, as you can see in the list below.

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## Simplification Of Boolean Function Part-IV

QUINE-McCLUSKEY MINIMIZATION

Quine-McCluskey minimization method uses the same theorem to produce the solution as the K-map method, namely X(Y+Y')=X

Minimization Technique

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## Simplification Of Boolean Functions Part-III

4-Variable K-Map

There are 16 cells in a 4-variable (W, X, Y, Z); K-map as shown in the figure below.

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## Simplification Of Boolean Functions Part-II

2-Variable K-Map

In any K-Map, each square represents a minterm. Adjacent squares always differ by just one literal (So that the unifying theorem may apply: X + X' = 1).

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## Simplification Of Boolean Functions Part-I

Introduction
Simplification of Boolean functions is mainly used to reduce the gate count of a design. Less number of gates means less power consumption, sometimes the circuit works faster and also when number of gates is reduced, cost also comes down.

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## Combinational Arithmetic Circuits Part-IV

Multipliers
Multiplication is achieved by adding a list of shifted multiplicands according to the digits of the multiplier. An n-bit X n-bit multiplier can be realized in combinational circuitry by using an array of n-1 n-bit adders where each adder is shifted by one position.

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## Combinational Arithmetic Circuits Part-III

Subtracter
Subtracter circuits take two binary numbers as input and subtract one binary number input from the other binary number input. Similar to adders, it gives out two outputs, difference and borrow (carry-in the case of Adder).

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## Combinational Arithmetic Circuits Part-II

An n-bit adder used to add two n-bit binary numbers can be built by connecting n full adders in series. Each full adder represents a bit position j (from 0 to n-1).

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## Combinational Arithmetic Circuits Part-I

Introduction

Arithmetic circuits are the ones which perform arithmetic operations like addition, subtraction, multiplication, division, parity calculation. Most of the time, designing these circuits is the same as designing muxers, encoders and decoders.

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## Digital Number System Part-V

Floating Point Numbers
A real number or floating point number is a number which has both an integer and a fractional part. Examples for real real decimal numbers are 123.45, 0.1234, -0.12345, etc. Examples for real binary numbers are 1100.1100, 0.1001, -1.001, etc. In general, floating point numbers are expressed in exponential notation.

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## Digital Number System Part-IV

Error Detecting and Correction Codes
For reliable transmission and storage of digital data, error detection and correction is required. Below are a few examples of codes which permit error detection and error correction after detection.

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## Digital Number System Part-III

Binary Codes
Binary codes are codes which are represented in binary system with modification from the original ones. Below we will be seeing the following:

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