Limitations of storing numbers

Integer Representation

Whole numbers without fractional components (e.g., 120, 10, 0, -20).

Binary Representation

Uses bits to store integers. Example:4-bit 0 111 represents 7.

Overflow

Exceeding the maximum storage capacity of a system. Example:In a 4-bit system, adding 1 to 7 causes overflow.

Floating-Point Representation

Represents non-integers using base 2. Example:64-bit system with 1 sign bit, 11 exponent bits, and 52 number bits.

Roundoff Errors

Precision loss due to inability to fully represent certain numbers in binary. Example:Adding 0.1 three times may not equal 0.3 exactly.

Modern Systems

64-bit architecture provides high precision for critical applications.