Understanding C Modulo Operator Output

This question asks about the output of a C program snippet that uses the modulo operator (%) with both positive and negative numbers. The modulo operator gives the remainder of a division.

In C, the sign of the result of the modulo operation a % b is the same as the sign of the dividend a.

Let's analyze each printf statement:

Calculating the First Output: 7 % -3

We need to find the remainder when 7 is divided by -3.

• First, perform integer division: \( \frac{7}{-3} \). In C, integer division truncates towards zero. \( \frac{7}{-3} \) is approximately -2.33, so truncation towards zero gives -2.
• The remainder is calculated using the formula: \( \text{remainder} = \text{dividend} - (\text{quotient} \times \text{divisor}) \)
• Substitute the values: \( \text{remainder} = 7 - (-2 \times -3) \)
• Calculate: \( \text{remainder} = 7 - (6) \)
• Result: \( \text{remainder} = 1 \)
• The sign of the dividend (7) is positive, so the sign of the result is positive.
• Therefore, 7 % -3 is 1.

Calculating the Second Output: -7 % 3

Now, we find the remainder when -7 is divided by 3.

• Perform integer division: \( \frac{-7}{3} \). In C, truncation towards zero gives -2 (since -2.33 truncated towards zero is -2).
• Calculate the remainder: \( \text{remainder} = \text{dividend} - (\text{quotient} \times \text{divisor}) \)
• Substitute the values: \( \text{remainder} = -7 - (-2 \times 3) \)
• Calculate: \( \text{remainder} = -7 - (-6) \)
• Result: \( \text{remainder} = -7 + 6 \)
• Result: \( \text{remainder} = -1 \)
• The sign of the dividend (-7) is negative, so the sign of the result is negative.
• Therefore, -7 % 3 is -1.

Determining the Final C Code Output Sequence

The code has two printf statements executing sequentially:

1. printf("%d", 7 % -3); prints the result of 7 % -3, which is 1.
2. printf("%d", -7 % 3); prints the result of -7 % 3, which is -1.

The output is printed consecutively without any space or newline character between them by the printf calls themselves. However, when presented in options, the values are often separated for clarity.

The first value printed is 1, and the second value printed is -1.

Summary of C Modulo Calculations

The program prints 1, followed immediately by -1. The sequence of printed values is 1 then -1.

Revision Table: Key C Modulo Operator Points

Additional Information: Modulo Operator Behavior

The behavior of the modulo operator with negative numbers can differ slightly between programming languages. While C and C++ typically follow the rule where the remainder's sign matches the dividend, some other languages might have different rules, such as always returning a positive remainder (like Python for negative divisors) or matching the sign of the divisor. Understanding the specific language's definition is important.

For example, in Python:

• 7 % -3 results in -2 (Python's modulo result sign matches the divisor when the divisor is negative).
• -7 % 3 results in 2 (Python's modulo result sign matches the divisor when the divisor is positive, but it's always non-negative if the divisor is positive).

This highlights why it's crucial to know the language specification when dealing with modulo operations involving negative operands.