C basics formulas

C fundamentals: types, operators, expressions and control flow. 4 formulas for GATE CS Programming in C, each with when to use it. Each is explained in the topic notes.

All 4 C basics formulas

N-BIT INTEGER RANGES

unsigned n -bit range : [0, 2^{n} - 1] signed (two’s complement) n -bit range : [- 2^{n - 1}, 2^{n - 1} - 1]

Holds for any fixed-width integer type once its width $n$ in bits and its signedness are known. Use it to check whether a constant fits the type it is stored in.

STORING AN OUT-OF-RANGE VALUE V IN A SIGNED N-BIT TYPE

r = v mod 2^{n} (0 \leq r \leq 2^{n} - 1), stored value = r r - 2^{n} if r \leq 2^{n - 1} - 1 otherwise

The standard leaves this conversion implementation-defined. On the two's complement machines these notes assume, the result is the value above. For example, 200 stored in a signed 8-bit char gives $200 - 256 = - 56$ . An unsigned $n$ -bit type always stores $r$ , and that case is defined by the standard.

TWO'S COMPLEMENT NEGATION AND UNSIGNED WRAPAROUND

- x \equiv (\sim x) + 1 (mod 2^{n}) a + b \equiv (a + b) mod 2^{n} for unsigned n -bit arithmetic

Here $\sim x$ is the bitwise complement. Arithmetic done in unsigned int (or a wider unsigned type) never overflows in the undefined-behaviour sense: it is defined to wrap modulo $2^{n}$ . Signed overflow, such as INT_MAX + 1, is undefined behaviour. Converting an out-of-range value to a signed type is implementation-defined (see the storing rule in the previous section).

INTEGER DIVISION IDENTITY IN C

a = (a / b) \cdot b + (a % b), a / b truncated toward 0 (b \neq = 0)

Holds for C integer operands when $a / b$ is representable. Truncation toward zero means that the sign of a % b follows the sign of a. Division or % by zero is undefined behaviour.

Where this was asked: 2018 (1), 2022 (1), 2024 (3), 2025 (2). See the 7 previous-year questions on C basics. This shows what was asked, not what will be asked.

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C basics: the notes and 7 solved previous-year questions