Logical values in MATLAB - Step-by-Step Execution

Concept Flow - Logical values

Start

↓

Create logical value

↓

Use in condition or operation

↓

Result: true (1) or false (0)

↓

End

Logical values in MATLAB represent true or false states, used in conditions and logical operations.

Execution Sample

MATLAB

a = true;
b = false;
c = a && b;
d = a || b;

This code creates logical values and uses AND and OR operations to combine them.

Execution Table

Step	Action	Expression	Result
1	Assign true to a	a = true	a = 1
2	Assign false to b	b = false	b = 0
3	Compute c as a AND b	c = a && b	c = 0
4	Compute d as a OR b	d = a || b	d = 1

💡 All logical assignments and operations completed.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4
a	undefined	1	1	1	1
b	undefined	undefined	0	0	0
c	undefined	undefined	undefined	0	0
d	undefined	undefined	undefined	undefined	1

Key Moments - 2 Insights

Why does c become 0 when a is true and b is false?

Because c is computed using AND (&&), which is true only if both a and b are true. Step 3 in the execution_table shows c = a && b results in 0.

Why is d equal to 1 even though b is false?

Because d uses OR (||), which is true if at least one operand is true. Step 4 shows d = a || b results in 1 since a is true.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of variable 'b' after Step 2?

A undefined

B 1

C 0

D true

💡 Hint

Check the 'Result' column for Step 2 where b is assigned false (0).

At which step does variable 'c' get its value assigned?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at the 'Action' column to find when c is computed.

If 'a' was false instead of true, what would be the value of 'd' after Step 4?

A 0

B 1

C undefined

D true

💡 Hint

Recall OR (||) is true if either operand is true; if both are false, result is false (0).

Concept Snapshot

Logical values in MATLAB are true (1) or false (0).
Use true and false keywords or 1 and 0.
Logical operators: && (AND), || (OR), ~ (NOT).
AND is true only if both are true.
OR is true if at least one is true.
Used in conditions and logical expressions.

Full Transcript

This lesson shows how MATLAB uses logical values true and false, represented as 1 and 0. We assign true to variable a and false to b. Then we compute c as a AND b, which results in false (0) because both must be true for AND to be true. Next, d is computed as a OR b, which results in true (1) because OR is true if either operand is true. The execution table traces each step and the variable tracker shows how variables change. Key moments clarify why c is false and d is true. The quiz tests understanding of variable values and logical operations.

Practice

1. What is the result of the expression 5 > 3 in MATLAB?

easy

A. 5

B. false

C. 3

D. true

Solution

1. Step 1: Understand the comparison operator

   The operator > checks if the left number is greater than the right number.

2. Step 2: Compare the numbers 5 and 3

   Since 5 is greater than 3, the expression returns true.

3. Final Answer:

   true -> Option D

4. Quick Check:

   5 > 3 = true [OK]

Hint: Greater than means left number bigger than right [OK]

Common Mistakes:

• Confusing true with the number 5
• Thinking it returns the bigger number
• Mixing up > and < operators

2. Which of the following is the correct way to create a logical true value in MATLAB?

easy

A. 1 == 1

B. 1 = 1

C. logical(0)

D. true

Solution

1. Step 1: Evaluate each option

   logical(0) returns false.
   1 = 1 causes syntax error (cannot assign to constant).
   true errors (function requires arguments like true()).
   1 == 1 returns true.

2. Step 2: Identify the working method

   Only 1 == 1 correctly creates a logical true value.

3. Final Answer:

   1 == 1 -> Option A

4. Quick Check:

   1 == 1 = true [OK]

Hint: Use == in comparisons to get logical true [OK]

Common Mistakes:

• logical(0) returns false
• Using = instead of == for comparison
• Omitting () on true()

3. What is the output of this MATLAB code?

val = (4 < 2) | (7 == 7);
disp(val);

medium

A. Error

B. 0

C. 1

D. [0 1]

Solution

1. Step 1: Evaluate each logical expression

   4 < 2 is false (0), 7 == 7 is true (1).

2. Step 2: Apply the OR operator (|)

   False OR True results in true (1).

3. Final Answer:

   1 -> Option C

4. Quick Check:

   (false OR true) = true = 1 [OK]

Hint: OR is true if any side is true [OK]

Common Mistakes:

• Confusing OR (|) with AND (&)
• Expecting vector output
• Misreading comparison operators

4. Identify the error in this MATLAB code:

if 5 = 5
    disp('Equal');
end

medium

A. Using single = instead of == in if condition

B. Missing semicolon after disp statement

C. Incorrect use of disp function

D. No error, code runs fine

Solution

1. Step 1: Check the if condition syntax

   The single equal sign = is for assignment, not comparison.

2. Step 2: Correct the comparison operator

   Use double equal signs == to compare values in conditions.

3. Final Answer:

   Using single = instead of == in if condition -> Option A

4. Quick Check:

   Comparison needs ==, not = [OK]

Hint: Use == for comparison, = for assignment [OK]

Common Mistakes:

• Using = in if condition
• Ignoring MATLAB error messages
• Assuming semicolon is mandatory after disp

5. Given the vector A = [-1 0 1 2 0], which MATLAB expression returns a logical vector indicating which elements are nonzero?

hard

A. All of the above

B. A ~= 0

C. A > 0

D. A != 0

Solution

1. Step 1: Understand each expression

   A ~= 0 returns true where not zero.
   A != 0 uses invalid != operator (use ~=).
   A > 0 true only for positives.

2. Step 2: Check which elements each marks true for A = [-1 0 1 2 0]

   - A ~= 0: [true, false, true, true, false]
   - A != 0: syntax error
   - A > 0: [false, false, true, true, false]

3. Final Answer:

   A ~= 0 -> Option B

4. Quick Check:

   A ~= 0 = nonzero logical vector [OK]

Hint: Use ~= 0 to find nonzero elements [OK]

Common Mistakes:

• Using != instead of ~=
• Confusing ~= with ==
• Assuming >0 misses negative nonzero