Signedness and Bit Masks

ABSTRACT

In C, the char type is often signed by default (depending on the compiler and architecture). This means the most significant bit (MSB) acts as a sign bit, leading to unexpected results when performing “greater than” or “less than” comparisons on raw byte values.

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1. The Signed Interpretation Error

When char is signed, it uses Two’s Complement representation. A byte like 0xFF is not interpreted as $255$, but as $-1$. The Comparison Breakdown:

• Logic: We want to check if a character is in the standard ASCII range ($0$–$127$).
• c <= 128: If c is 0xFF (signed $-1$), the expression -1 <= 128 evaluates to True.
• c & 0b10000000: This checks if the 8th bit is set. If 0xFF is masked, the result is 0b10000000, which is not 0. This correctly identifies that the value is outside the standard 7-bit ASCII range.

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2. The Truth Table Analysis

The discrepancy arises because the Bitwise AND looks at the raw bits, while the “Less Than” operator looks at the numerical value interpreted by the type.

Input (Hex)	Binary	Signed Value	c < 128	(c & 0x80) == 0
0x48	01001000	72	True (1)	True (1)
0xFF	11111111	-1	True (1)	False (0)
0x0A	00001010	10	True (1)	True (1)

IMPORTANT

Because -1 is less than 128, the “Less Than” check fails to catch non-ASCII characters if the input is treated as a signed integer.

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3. The Fix: Explicit Casting

To ensure the comparison treats the byte as a value from $0$–$255$, you must cast the variable to an unsigned char.

int8_t is_ascii_lessthan(char c){
    // Casting to unsigned char forces the interpretation of 0xFF as 255
    return ((unsigned char) c) < 128;
}

By casting to unsigned, 0xFF becomes $255$. The expression 255 < 128 correctly evaluates to False (0), aligning the behavior of the numerical check with the bitwise check.

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4. Summary of Bitwise vs. Numerical Checks

• Bitwise AND (&): Generally safer for checking specific bit patterns (like the “High Bit” in ASCII) because it ignores signedness.
• Numerical Comparisons (<, >): Faster and more readable, but require careful attention to whether the type is signed or unsigned.