Logical operators (&, |, ~) in MATLAB - Step-by-Step Execution

Concept Flow - Logical operators (&, |, ~)

Start with two logical values A and B

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Apply AND (&) operator: A & B

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Apply OR (|) operator: A | B

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Apply NOT (~) operator: ~A or ~B

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Get final logical results

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End

Start with two logical values, then apply AND, OR, and NOT operators step-by-step to get logical results.

Execution Sample

MATLAB

A = [1 0 1];
B = [0 1 1];
C_and = A & B;
C_or = A | B;
C_not = ~A;

This code applies logical AND, OR, and NOT operators element-wise on arrays A and B.

Execution Table

Step	Operation	Operands	Result
1	Initialize A	[1 0 1]	A = [1 0 1]
2	Initialize B	[0 1 1]	B = [0 1 1]
3	AND (&)	A & B	[0 0 1]
4	OR (|)	A | B	[1 1 1]
5	NOT (~)	~A	[0 1 0]

💡 All operations complete element-wise on arrays; logical results obtained.

Variable Tracker

Variable	Start	After Step 3	After Step 4	After Step 5
A	[1 0 1]	[1 0 1]	[1 0 1]	[1 0 1]
B	[0 1 1]	[0 1 1]	[0 1 1]	[0 1 1]
C_and	N/A	[0 0 1]	[0 0 1]	[0 0 1]
C_or	N/A	N/A	[1 1 1]	[1 1 1]
C_not	N/A	N/A	N/A	[0 1 0]

Key Moments - 2 Insights

Why does the AND operation result in [0 0 1] when A is [1 0 1] and B is [0 1 1]?

Because AND (&) returns 1 only if both corresponding elements are 1. Here, only the last elements of A and B are both 1, so only the last result is 1 (see execution_table step 3).

What does the NOT (~) operator do to the array A?

The NOT (~) operator flips each element: 1 becomes 0, and 0 becomes 1. So ~A changes [1 0 1] to [0 1 0] as shown in execution_table step 5.

Visual Quiz - 3 Questions

Look at the execution table, what is the result of the OR (|) operation at step 4?

A [1 1 1]

B [0 0 1]

C [0 1 0]

D [1 0 1]

💡 Hint

Check the 'Result' column in execution_table row for step 4.

At which step does the variable C_and get its value assigned?

A Step 2

B Step 4

C Step 3

D Step 5

💡 Hint

Look at the 'Operation' column in execution_table where AND (&) is applied.

If A was [0 0 0], what would be the result of ~A according to the variable_tracker logic?

A [0 1 0]

B [1 1 1]

C [0 0 0]

D [1 0 1]

💡 Hint

NOT (~) flips each element; see variable_tracker row for C_not.

Concept Snapshot

Logical operators in MATLAB:
& (AND): true if both true
| (OR): true if any true
~ (NOT): flips true/false
Operate element-wise on arrays
Use for logical indexing and conditions

Full Transcript

This visual execution trace shows how MATLAB logical operators work on arrays. Starting with two arrays A and B, the AND operator (&) compares each element pair and returns 1 only if both are 1. The OR operator (|) returns 1 if either element is 1. The NOT operator (~) flips each element from 1 to 0 or 0 to 1. The execution table tracks each step and result, while the variable tracker shows how variables change. Key moments clarify why AND returns [0 0 1] and how NOT flips values. The quiz tests understanding of these steps and results.