Operator Precedence | GCE AL ICT | Unit 4 | Boolean Logic and Digital Circuit | in Tamil | English and தமிழில் Medium Notes Questions

AL ICT – Unit 4: Boolean Logic & Digital Circuits

Operator Precedence (Beginner Friendly Explanation)

This lesson explains Operator Precedence in Boolean Logic step by step, using simple examples from the AL ICT syllabus.

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1. What is Operator Precedence?

Operator precedence means the order in which operations are performed in a Boolean expression.

Just like in Mathematics, some operations are done before others.

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2. BODMAS Rule (Revision)

In Mathematics, we use BODMAS:

• B – Brackets
• O – Orders (powers, roots)
• D – Division
• M – Multiplication
• A – Addition
• S – Subtraction

Example:

2 + 3 × 4 = 14 (not 20, because multiplication is done first)

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3. Boolean Operator Precedence (AL ICT)

In Boolean Algebra, the precedence order is:

1. NOT ( ' )
2. AND ( . )
3. OR ( + )
4. XOR ( ⊕ )

Brackets ( ) always have highest priority.

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4. Understanding Basic Boolean Operators

• AND ( . ) → Both must be TRUE
• OR ( + ) → At least one TRUE
• NOT ( ' ) → Reverse the value
• XOR ( ⊕ ) → Only one TRUE (not both)

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5. Expression: x + y.z

According to precedence, AND (.) is done before OR (+).

Step-by-step:

1. First calculate y.z
2. Then add x + (result)

So:

x + y.z = x + (y.z)

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6. Expression: (x + y).z

Brackets have the highest priority.

Steps:

1. Solve inside the bracket → x + y
2. Then AND with z

So:

(x + y).z

Note: This is NOT the same as x + y.z

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7. Expression: x + y ⊕ z.x

Operator precedence:

1. AND (.)
2. XOR (⊕)
3. OR (+)

Steps:

1. First calculate z.x
2. Then calculate y ⊕ (z.x)
3. Finally calculate x + (result)

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8. Real-Life Example (Road Crossing)

Boolean Function:

F = X.Y + Z

Meaning:

• X = Right side clear
• Y = Left side clear
• Z = Signal light OFF

Interpretation:

You can cross the road if:

• Right side AND Left side are clear, OR
• Signal light is OFF

Why AND first? Because both sides must be clear.

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9. How to Make a Truth Table

Step 1: Identify Inputs

Inputs are variables like X, Y, Z

If you have:

X and X'

Still only ONE input (X), because X' is just NOT X.

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Step 2: Number of Rows

Formula:

2ⁿ (n = number of inputs)

• 1 input → 2 rows
• 2 inputs → 4 rows
• 3 inputs → 8 rows

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Step 3: Fill Input Values

X	Y
0	0
0	1
1	0
1	1

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10. Boolean Function Components

LHS and RHS

Example:

F = X.Y + Z

• LHS → F
• RHS → X.Y + Z

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Operators

• +
• .
• '
• ⊕

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Variables

X, Y, Z

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Terms

Separated by OR (+)

Example:

X.Y + Z → Terms are:

• X.Y
• Z

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11. Min Term (SOP – Sum of Products)

Min Term:

• Uses AND between variables
• All variables appear

Example:

X'.Y.Z

SOP = Sum (OR) of product (AND) terms

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12. Max Term (POS – Product of Sums)

Max Term:

• Uses OR between variables
• All variables appear

Example:

(X + Y' + Z)

POS = Product (AND) of sum (OR) terms

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13. Standard Boolean Functions

• Standard SOP → Only min terms
• Standard POS → Only max terms

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14. Practice Questions

1. Find the precedence order in: X + Y.Z'
2. Rewrite using brackets: X + Y.Z
3. Identify inputs in: A + A'
4. Write SOP form for: F = X.Y + X'.Z

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Truth Table for F = (X'.Y') + (X' + Y')

X	Y	X'	Y'	X'.Y'	X' + Y'	F
0	0	1	1	1	1	1
0	1	1	0	0	1	1
1	0	0	1	0	1	1
1	1	0	0	0	0	0

Final Output Column (F): 1, 1, 1, 0

Truth Table for F = AB C' + A'B' C

A	B	C	C'	AB C'	A'B' C	F
0	0	0	1	0	0	0
0	0	1	0	0	1	1
0	1	0	1	0	0	0
0	1	1	0	0	0	0
1	0	0	1	0	0	0
1	0	1	0	0	0	0
1	1	0	1	1	0	1
1	1	1	0	0	0	0

Truth Table for F = X'.Y + (X + Z')

X	Y	Z	X'	Z'	X'.Y	X + Z'	F
0	0	0	1	1	0	1	1
0	0	1	1	0	0	0	0
0	1	0	1	1	1	1	1
0	1	1	1	0	1	0	1
1	0	0	0	1	0	1	1
1	0	1	0	0	0	1	1
1	1	0	0	1	0	1	1
1	1	1	0	0	0	1	1

Truth Table for F = X + (Y ⊕ X.Z)

X	Y	Z	X.Z	Y ⊕ X.Z	F
0	0	0	0	0	0
0	0	1	0	0	0
0	1	0	0	1	1
0	1	1	0	1	1
1	0	0	0	0	1
1	0	1	1	1	1
1	1	0	0	1	1
1	1	1	1	0	1

End of Lesson – Unit 4 Boolean Logic