Bitwise NOT in C - Step-by-Step Execution

Concept Flow - Bitwise NOT

Start with integer value

↓

Apply bitwise NOT (~) operator

↓

Flip each bit: 0->1, 1->0

↓

Result is new integer with flipped bits

↓

Use or print the result

↓

End

The bitwise NOT operator flips every bit of an integer, turning 0s into 1s and 1s into 0s, producing a new integer.

Execution Sample

C

int x = 5;
int y = ~x;
printf("%d", y);

This code flips all bits of 5 and prints the resulting integer.

Execution Table

Step	Variable	Value (decimal)	Value (binary 8-bit)	Operation	Result (binary)	Result (decimal)
1	x	5	00000101	Initial value	00000101	5
2	y	N/A	N/A	Apply ~x (bitwise NOT)	11111010	-6
3	y	-6	11111010	Print y	11111010	-6

💡 Program ends after printing the bitwise NOT of 5, which is -6 in two's complement.

Variable Tracker

Variable	Start	After Step 2	Final
x	5	5	5
y	undefined	-6	-6

Key Moments - 2 Insights

Why does ~5 become -6 instead of a large positive number?

Because integers use two's complement representation, flipping bits of 5 (00000101) results in 11111010, which is -6 in two's complement. See execution_table step 2.

Why do we show 8 bits in binary when integers are usually 32 bits?

For simplicity and clarity, we show 8 bits here. The actual integer has more bits, but the principle of flipping each bit is the same. The sign bit determines if the number is negative.

Visual Quiz - 3 Questions

Look at the execution_table, what is the binary result of applying ~ to 5?

A 00000101

B 11111010

C 11111101

D 00011010

💡 Hint

Check the 'Result (binary)' column in step 2 of execution_table.

At which step is the variable y assigned a value?

A Step 2

B Step 1

C Step 3

D Never

💡 Hint

Look at the 'Operation' column where ~x is applied and y gets its value.

If x was 0 instead of 5, what would be the decimal value of ~x?

A 1

B 0

C -1

D -0

💡 Hint

Remember that ~0 flips all bits to 1, which is -1 in two's complement.

Concept Snapshot

Bitwise NOT (~) flips every bit of an integer.
Example: ~5 flips 00000101 to 11111010.
In two's complement, this results in -6.
Useful for low-level bit manipulation.
Always remember sign bit affects result.

Full Transcript

The bitwise NOT operator (~) takes an integer and flips all its bits. For example, starting with 5, which is 00000101 in binary (8-bit shown for simplicity), applying ~ flips every bit to 11111010. In two's complement representation, this binary number equals -6. The program stores this result in variable y and prints it. This shows how bitwise NOT changes positive numbers into negative ones by flipping bits, including the sign bit. Understanding two's complement is key to interpreting the result correctly.

Practice

1. What does the bitwise NOT operator ~ do to an integer in C?

easy

A. It adds 1 to the integer.

B. It shifts all bits to the left by one position.

C. It sets all bits to zero.

D. It flips every bit of the integer, changing 0s to 1s and 1s to 0s.

Solution

1. Step 1: Understand the bitwise NOT operator

   The bitwise NOT operator ~ in C flips every bit of the integer. This means all 0 bits become 1, and all 1 bits become 0.

2. Step 2: Compare with other bitwise operations

   Unlike shifting or adding, ~ only toggles bits without changing their positions or values numerically.

3. Final Answer:

   It flips every bit of the integer, changing 0s to 1s and 1s to 0s. -> Option D

4. Quick Check:

   Bitwise NOT = flip bits [OK]

Hint: Remember: ~ flips bits, not shifts or adds [OK]

Common Mistakes:

• Confusing ~ with bit shift operators << or >>
• Thinking ~ adds or subtracts from the number
• Assuming ~ sets bits to zero instead of flipping

2. Which of the following is the correct syntax to apply bitwise NOT to an integer variable x in C?

easy

A. int y = ~x;

B. int y = not x;

C. int y = !x;

D. int y = x~;

Solution

1. Step 1: Recall the bitwise NOT operator syntax

   In C, the bitwise NOT operator is the tilde symbol ~ placed before the variable.

2. Step 2: Check each option

   int y = not x; uses not which is not valid in C. int y = !x; uses logical NOT !. int y = x~; has incorrect placement of ~. Only int y = ~x; correctly uses ~x.

3. Final Answer:

   int y = ~x; -> Option A

4. Quick Check:

   Bitwise NOT syntax = ~x [OK]

Hint: Use ~ before variable for bitwise NOT [OK]

Common Mistakes:

• Using 'not' instead of ~
• Confusing logical NOT (!) with bitwise NOT (~)
• Placing ~ after the variable

3. What is the output of the following C code?

int x = 5;
int y = ~x;
printf("%d", y);

medium

A. 5

B. -6

C. -5

D. 6

Solution

1. Step 1: Convert 5 to binary and apply bitwise NOT

   5 in binary (32-bit) is 00000000 00000000 00000000 00000101. Applying ~ flips bits to 11111111 11111111 11111111 11111010.

2. Step 2: Interpret the result as a signed integer

   The result is the two's complement representation of -6.

3. Final Answer:

   -6 -> Option B

4. Quick Check:

   ~5 = -6 in two's complement [OK]

Hint: ~x equals -(x+1) for signed integers [OK]

Common Mistakes:

• Thinking ~5 equals 6 instead of -6
• Ignoring two's complement representation
• Confusing bitwise NOT with logical NOT

4. Identify the error in the following C code snippet:

int x = 10;
int y = ~ x;
printf("%d", y);

medium

A. There is a syntax error due to space between ~ and x.

B. The code will print 9 instead of expected -11.

C. No error; the code works and prints -11.

D. The printf format specifier is incorrect.

Solution

1. Step 1: Check syntax of bitwise NOT usage

   In C, spaces between operators and operands are allowed. So ~ x is valid and equivalent to ~x.

2. Step 2: Verify output and printf usage

   Applying ~10 results in -11. The printf format specifier %d is correct for int.

3. Final Answer:

   No error; the code works and prints -11. -> Option C

4. Quick Check:

   Space allowed after ~, output = -11 [OK]

Hint: Spaces don't break ~ operator usage [OK]

Common Mistakes:

• Thinking space causes syntax error
• Expecting positive output instead of negative
• Confusing format specifier for int

5. Given a signed 8-bit integer n, which expression correctly computes the bitwise NOT of n and then adds 1, effectively calculating the two's complement negation of n in C?

hard

A. ~n + 1

B. ~(n + 1)

C. -~n

D. -n + 1

Solution

1. Step 1: Understand two's complement negation

   Two's complement negation of a number n is computed as ~n + 1.

2. Step 2: Analyze each option

   ~n + 1 matches the formula. ~(n + 1) negates after adding 1, which is incorrect. -~n negates the bitwise NOT, not the number. -n + 1 is arithmetic negation plus 1, which is not two's complement negation.

3. Final Answer:

   ~n + 1 -> Option A

4. Quick Check:

   Two's complement negation = ~n + 1 [OK]

Hint: Two's complement negation = ~n + 1 [OK]

Common Mistakes:

• Using -(~n) instead of ~n + 1
• Applying ~ after adding 1
• Confusing arithmetic negation with bitwise negation