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We begin this session with an example to understand the impact of 0s and 1s in our lives.
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Suppose you are handed with a will of 1000 dollars.
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The money increases if we increase zeroes on the right.
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However, if we swap the one to right, the values decreases drastically.
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This is numerical significance whereas in smart devices, it has a logical significance.
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The values are decisions which can have a high value or logic 1
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and a low value or logic 0.
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The decision-making elements are called logic gates.
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The decisions are termed as output which are binary variables 0 or 1.
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It has a single output.
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The input to logic gate can be single or multiple.
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The output changes for every input combination and it depends upon two things -
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Type of logic gate and nature of input variables.
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There are numerous gates available, each for a specific decision.
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Each of these have a specific symbol and clearly defined behaviour.
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There are two major classifications- Basic gates and derived gates.
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We will discuss each of them in detail later.
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For now, let's concentrate upon the nature of binary input variables.
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To study this, let's understand the truth table.
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It maps the input-output relationship.
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The left hand side, lists all possible combinations of input binary variables
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and RHS maps the output to each.
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Consider a logic gate with a single input A.
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It can take values 0 or 1.
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There are 2 input combinations for 1 input variable.
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Another system has two inputs,
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A and B and a single output Y.
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It may happen that A has the value 0 and B takes values
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0 or 1.
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When A is at logic 1, B may have values 0 or 1.
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Thus there are 4 input combinations for 2 input variables.
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Therefore, n input variables will have 2^n input combinations.
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There is a trick to fill the truth table.
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We start filling with the leftmost input and will go column by column.
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Since we know it will have four input combinations,
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2 zeroes are followed by 2 ones.
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Next column with have one zero followed by one one.
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If there are 3 inputs A, B, and C,
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there will be 2^3 = 8 combinations.
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Left most column will have 4 zeroes, 4 ones.
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Next column will have 2 zeroes, 2 ones
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which will repeat.
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Last column will have a series of 0 and 1.
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But how do we decide the output for each input?
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The type of logic gate decides the output.
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Let us study the basic logic gates.
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Basic logic gates are the fundamental logical operations
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from which all other functions
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no matter how complex can be derived.
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These functions are named as AND, OR and NOT.
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The first basic gate is an AND gate.
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This is the symbol for AND Gate.
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A and B are two inputs resulting in a single output Y.
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The Boolean expression is read as Y = A and B..
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A Boolean expression relates output with the inputs of the logic system
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For a 3 input AND gate, the boolean expression is Y=A and B and C.
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This way the boolean expression can be written for a multiple input AND gate.
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Let's construct the truth table. When both
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When both the inputs A and B are low,
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the output Y is low.
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The output of AND Gate is low when either
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of the inputs are low.
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Both the inputs A, B need to be at logic 1
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for the output to be 1
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You can imagine it as 2 switches in series.
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When the circuit is complete, the bulb will glow.
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When both the switches are at logic 1, the path is complete and current
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flows. AND Gate finds applications in security systems such as burglar's alarm.
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Suppose you have to leave the house and keep the house secure.
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You turn on the alarm switch.
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This turns first input of AND gate as high.
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If a burglar tries to enter the house,
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the person sensor detects a logic 1.
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This goes to second input of AND gate.
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When both the inputs are
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high, the output of AND gate is high which sets the alarm ON.
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Second type of basic gate is an OR gate.
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For two inputs A and B, the Boolean expression
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is A OR B.
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For multiple input, It is simply this way.
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Let us see the truth table.
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For two input OR gate
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when both the inputs are low the output is low
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otherwise the output
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is high for remaining 3 input combinations.
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It is similar to 2 switches in parallel.
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The circuit is complete when either of the inputs is at logic 1 or both at logic 1 which makes the bulb glow.
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When a house has a front door and a back door, guests can arrive at any door
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In the event, when either the front door or the back door bell is pressed, the
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bell rings indicating that the guest has arrived.
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The last basic gate is a NOT gate. This gate can only have one input.
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Let us consider the input as A
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As the name suggests, the output is always NOT the input i.e., complement of input.
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A complement is denoted by a bar over the variable. The boolean expression for input, A is A bar.
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When the input is 0, output is 1 and vice versa