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  • We begin this session with an example to understand the impact of 0s and 1s in our lives.

  • Suppose you are handed with a will of 1000 dollars.

  • The money increases if we increase zeroes on the right.

  • However, if we swap the one to right, the values decreases drastically.

  • This is numerical significance whereas in smart devices, it has a logical significance.

  • The values are decisions which can have a high value or logic 1

  • and a low value or logic 0.

  • The decision-making elements are called logic gates.

  • The decisions are termed as output which are binary variables 0 or 1.

  • It has a single output.

  • The input to logic gate can be single or multiple.

  • The output changes for every input combination and it depends upon two things -

  • Type of logic gate and nature of input variables.

  • There are numerous gates available, each for a specific decision.

  • Each of these have a specific symbol and clearly defined behaviour.

  • There are two major classifications- Basic gates and derived gates.

  • We will discuss each of them in detail later.

  • For now, let's concentrate upon the nature of binary input variables.

  • To study this, let's understand the truth table.

  • It maps the input-output relationship.

  • The left hand side, lists all possible combinations of input binary variables

  • and RHS maps the output to each.

  • Consider a logic gate with a single input A.

  • It can take values 0 or 1.

  • There are 2 input combinations for 1 input variable.

  • Another system has two inputs,

  • A and B and a single output Y.

  • It may happen that A has the value 0 and B takes values

  • 0 or 1.

  • When A is at logic 1, B may have values 0 or 1.

  • Thus there are 4 input combinations for 2 input variables.

  • Therefore, n input variables will have 2^n input combinations.

  • There is a trick to fill the truth table.

  • We start filling with the leftmost input and will go column by column.

  • Since we know it will have four input combinations,

  • 2 zeroes are followed by 2 ones.

  • Next column with have one zero followed by one one.

  • If there are 3 inputs A, B, and C,

  • there will be 2^3 = 8 combinations.

  • Left most column will have 4 zeroes, 4 ones.

  • Next column will have 2 zeroes, 2 ones

  • which will repeat.

  • Last column will have a series of 0 and 1.

  • But how do we decide the output for each input?

  • The type of logic gate decides the output.

  • Let us study the basic logic gates.

  • Basic logic gates are the fundamental logical operations

  • from which all other functions

  • no matter how complex can be derived.

  • These functions are named as AND, OR and NOT.

  • The first basic gate is an AND gate.

  • This is the symbol for AND Gate.

  • A and B are two inputs resulting in a single output Y.

  • The Boolean expression is read as Y = A and B..

  • A Boolean expression relates output with the inputs of the logic system

  • For a 3 input AND gate, the boolean expression is Y=A and B and C.

  • This way the boolean expression can be written for a multiple input AND gate.

  • Let's construct the truth table. When both

  • When both the inputs A and B are low,

  • the output Y is low.

  • The output of AND Gate is low when either

  • of the inputs are low.

  • Both the inputs A, B need to be at logic 1

  • for the output to be 1

  • You can imagine it as 2 switches in series.

  • When the circuit is complete, the bulb will glow.

  • When both the switches are at logic 1, the path is complete and current

  • flows. AND Gate finds applications in security systems such as burglar's alarm.

  • Suppose you have to leave the house and keep the house secure.

  • You turn on the alarm switch.

  • This turns first input of AND gate as high.

  • If a burglar tries to enter the house,

  • the person sensor detects a logic 1.

  • This goes to second input of AND gate.

  • When both the inputs are

  • high, the output of AND gate is high which sets the alarm ON.

  • Second type of basic gate is an OR gate.

  • For two inputs A and B, the Boolean expression

  • is A OR B.

  • For multiple input, It is simply this way.

  • Let us see the truth table.

  • For two input OR gate

  • when both the inputs are low the output is low

  • otherwise the output

  • is high for remaining 3 input combinations.

  • It is similar to 2 switches in parallel.

  • The circuit is complete when either of the inputs is at logic 1 or both at logic 1 which makes the bulb glow.

  • When a house has a front door and a back door, guests can arrive at any door

  • In the event, when either the front door or the back door bell is pressed, the

  • bell rings indicating that the guest has arrived.

  • The last basic gate is a NOT gate. This gate can only have one input.

  • Let us consider the input as A

  • As the name suggests, the output is always NOT the input i.e., complement of input.

  • A complement is denoted by a bar over the variable. The boolean expression for input, A is A bar.

  • When the input is 0, output is 1 and vice versa

We begin this session with an example to understand the impact of 0s and 1s in our lives.

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基本のロジックゲートとは?| デジタルゲートの基本を6分で学ぶ|AND、OR、NOTゲート|DE.10 (What are Basic logic gates? | Learn basic digital gates in 6 min | AND, OR and NOT gates | DE.10)

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    Henry 楊 に公開 2021 年 01 月 14 日
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