Numeric types (double, single, integer) in MATLAB - Step-by-Step Execution

Concept Flow - Numeric types (double, single, integer)

Start: Assign numeric value

↓

Choose numeric type

↓

Double

↓

Store value in memory with type

↓

Use value in calculations

↓

End

This flow shows how MATLAB assigns a numeric value to a variable, chooses its type (double, single, or integer), stores it accordingly, and uses it in calculations.

Execution Sample

MATLAB

a = 5;          % default is double
b = single(5);   % single precision
c = int32(5);    % 32-bit integer

This code assigns the number 5 to three variables with different numeric types: double (default), single, and 32-bit integer.

Execution Table

Step	Variable	Value Assigned	Type	Memory Size (bytes)	Notes
1	a	5	double	8	Default numeric type in MATLAB is double precision
2	b	5	single	4	Single precision uses less memory than double
3	c	5	int32	4	Integer type stores whole numbers only
4	Use a + b	10	double	8	Result promoted to double for calculation
5	Use c + 2	7	int32	4	Result remains int32 for calculation
6	End	-	-	-	Execution ends after assignments and calculations

💡 All variables assigned and used; MATLAB ends execution.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	Final
a	undefined	5 (double)	5 (double)	5 (double)	5 (double)
b	undefined	undefined	5 (single)	5 (single)	5 (single)
c	undefined	undefined	undefined	5 (int32)	5 (int32)

Key Moments - 3 Insights

Why does variable 'a' use 8 bytes of memory while 'b' uses 4 bytes?

Because 'a' is of type double which uses 8 bytes for higher precision, while 'b' is single precision which uses 4 bytes, as shown in execution_table rows 1 and 2.

What happens if you add a double and a single type variable?

MATLAB promotes the result to double type for precision, as shown in execution_table row 4 where 'a + b' results in a double.

Can integer variables store decimal numbers?

No, integer types like int32 store only whole numbers. Decimal parts are truncated or cause errors, as implied in execution_table row 3.

Visual Quiz - 3 Questions

Look at the execution_table at step 2. What is the type and memory size of variable 'b'?

A single, 4 bytes

B double, 8 bytes

C int32, 4 bytes

D single, 8 bytes

💡 Hint

Check the 'Type' and 'Memory Size' columns for step 2 in the execution_table.

At which step does MATLAB promote the result to double type during addition?

A Step 3

B Step 4

C Step 5

D Step 2

💡 Hint

Look at the 'Notes' column in execution_table for the step where 'a + b' is calculated.

If variable 'c' was assigned as int16 instead of int32, what would change in the execution_table?

A Type would remain int32

B Value would change from 5 to 16

C Memory size would be 2 bytes instead of 4 bytes

D Variable 'c' would become double

💡 Hint

Check the 'Memory Size' column for int32 and recall int16 uses less memory.

Concept Snapshot

Numeric types in MATLAB:
- Default is double (8 bytes, high precision)
- single uses 4 bytes, less precision
- Integer types (int8, int16, int32, int64) store whole numbers
- Operations may promote types (e.g., single + double -> double)
- Choose type based on precision and memory needs

Full Transcript

This lesson shows how MATLAB handles numeric types: double, single, and integer. Variables 'a', 'b', and 'c' are assigned the value 5 but with different types. Double is default and uses 8 bytes, single uses 4 bytes, and int32 is a 4-byte integer type. When adding double and single, MATLAB promotes the result to double for precision. Integer types store only whole numbers. Memory size and type affect precision and storage. Understanding these helps choose the right type for your data.

Practice

1. Which numeric type is the default in MATLAB when you create a number like 5 without specifying its type?

easy

A. single

B. uint8

C. int32

D. double

Solution

1. Step 1: Understand MATLAB default numeric type

   By default, MATLAB stores numbers as double precision floating-point values.

2. Step 2: Check the given number type

   The number 5 without any type specification is stored as double.

3. Final Answer:

   double -> Option D

4. Quick Check:

   Default numeric type = double [OK]

Hint: Remember: MATLAB defaults to double unless specified [OK]

Common Mistakes:

• Thinking single is default
• Confusing integer types as default
• Assuming uint8 is default

2. Which of the following is the correct way to create a single precision number with value 3.14 in MATLAB?

easy

A. x = single(3.14);

B. x = double(3.14);

C. x = int32(3.14);

D. x = single '3.14';

Solution

1. Step 1: Identify correct syntax for single precision

   Use the function single() with a numeric argument to create a single precision number.

2. Step 2: Check each option

   x = single(3.14); uses single(3.14) which is correct syntax. x = double(3.14); creates double, not single. x = int32(3.14); creates integer, which truncates decimals. x = single '3.14'; is invalid syntax.

3. Final Answer:

   x = single(3.14); -> Option A

4. Quick Check:

   Use single() function for single precision [OK]

Hint: Use single() function to convert numbers to single [OK]

Common Mistakes:

• Using double() instead of single()
• Trying to assign string to single
• Using int32 for decimals

3. What will be the output of the following MATLAB code?

x = int8(127); y = x + 1; disp(y);

medium

A. -128

B. 128

C. Error: Overflow

D. 127

Solution

1. Step 1: Understand int8 range

   int8 stores integers from -128 to 127. Adding 1 to 127 causes overflow.

2. Step 2: Check overflow behavior

   In MATLAB, int8 overflow wraps around to the minimum value, so 127 + 1 becomes -128.

3. Final Answer:

   -128 -> Option A

4. Quick Check:

   int8 overflow wraps to -128 [OK]

Hint: int8 max is 127; adding 1 wraps to -128 [OK]

Common Mistakes:

• Expecting 128 (out of range)
• Expecting error on overflow
• Thinking value stays at 127

4. Consider this MATLAB code:

a = single(1.5); b = int16(a); disp(b);

What is the output and why?

medium

A. 1.5

B. 1

C. 2

D. Error: Cannot convert single to int16

Solution

1. Step 1: Convert single to int16 behavior

   When converting from single to int16, MATLAB truncates the decimal part (does not round).

2. Step 2: Apply truncation to 1.5

   Truncating 1.5 results in 1, so b becomes 1.

3. Final Answer:

   1 -> Option B

4. Quick Check:

   Conversion truncates decimals, so 1.5 -> 1 [OK]

Hint: Conversion truncates decimals, no rounding [OK]

Common Mistakes:

• Expecting rounding to 2
• Expecting error on conversion
• Expecting output as 1.5

5. You want to store a large array of numbers between 0 and 255 efficiently in MATLAB. Which numeric type should you choose to minimize memory while preserving all values exactly?

hard

A. double

B. single

C. uint8

D. int16

Solution

1. Step 1: Identify value range and memory needs

   Values are between 0 and 255, so an unsigned 8-bit integer (uint8) fits exactly.

2. Step 2: Compare types for memory and precision

   double and single use more memory and are floating-point. int16 uses 16 bits and allows negative values, wasting space.

3. Step 3: Choose the best type

   uint8 uses 8 bits, stores 0-255 exactly, and saves memory.

4. Final Answer:

   uint8 -> Option C

5. Quick Check:

   Use uint8 for 0-255 integer range to save memory [OK]

Hint: Use uint8 for 0-255 integers to save memory [OK]

Common Mistakes:

• Choosing double wastes memory
• Using int16 wastes space and allows negatives
• Using single loses integer precision