Bitwise NOT in C

Introduction

Bitwise NOT flips every bit in a number from 0 to 1 or from 1 to 0. It helps us quickly invert bits for tasks like toggling flags or creating masks.

You want to invert all bits of a number to get its complement.

You need to toggle bits in a binary flag to switch states.

You want to create a mask that excludes certain bits.

You are working with low-level hardware or embedded systems where bit manipulation is common.

Syntax

C

int bitwise_not = ~number;

The ~ operator flips every bit of the integer 'number'.

The result depends on the size of the integer and uses two's complement representation.

Examples

Flips the lower 4 bits from 1 to 0 and upper bits from 0 to 1.

C

int number = 0b00001111;
int result = ~number;  // result flips bits of 00001111

All bits of zero become 1, resulting in -1 in two's complement.

C

int number = 0;
int result = ~number;  // flips all bits of 0

All bits of -1 are 1, flipping them results in 0.

C

int number = -1;
int result = ~number;  // flips all bits of -1

Sample Program

This program shows how bitwise NOT flips all bits of the number 15. The output shows the original and inverted values.

C

#include <stdio.h>

int main() {
    int original_number = 15;  // binary: 00000000 00000000 00000000 00001111
    int inverted_number = ~original_number;

    printf("Original number: %d\n", original_number);
    printf("Inverted number (bitwise NOT): %d\n", inverted_number);

    return 0;
}

Important Notes

Time complexity is O(1) because bitwise NOT operates on fixed-size integers directly.

Space complexity is O(1) as no extra memory is needed beyond variables.

Common mistake: forgetting that bitwise NOT results depend on integer size and signed representation, so the result may be negative.

Use bitwise NOT when you need to invert bits quickly; for arithmetic negation, use the unary minus operator (-).

Summary

Bitwise NOT (~) flips every bit of an integer.

It is useful for toggling bits and creating bit masks.

The result depends on the integer size and two's complement representation.

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