Decimal
Signed Binary
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In a computer, everything is represented by a sequence of bits, but those bits have no intrinsic meaning: we assign it through representations. While raw binary is enough for natural numbers, handling negative numbers and real values requires specific encodings. Noverflow allows you to analyze how "human" numbers are transformed into binary data, ready to be processed by a CPU or stored in RAM.
Support for Signed Magnitude, 1's Complement (C1), and 2's Complement (C2). The system automatically handles sign extension and algebraic value calculation based on the Most Significant Bit (MSB).
Management of real numbers via binary scientific notation. The module analyzes the breakdown into Sign, Exponent, and Mantissa, correctly applying Bias values for 32-bit (Single Precision) and 64-bit (Double Precision) formats.
Two's Complement is the standard representation in modern processors (x86, ARM). Its main advantage is the ability to perform subtractions using the same hardware as addition.
Calculation Procedure: To represent a negative number, start with its positive binary value, perform bit-flipping (1's complement), and add 1 to the Least Significant Bit (LSB). This eliminates "negative zero" ambiguity and maximizes the register's numerical range.
While less efficient, these forms are essential for understanding the evolution of computing.
In Signed Binary (analogous to Signed Magnitude), the leftmost bit (MSB) acts as a switch (0 for positive, 1 for negative).
One's Complement consists of logically inverting every bit for negative numbers; although simpler than C2, it suffers from the "double zero" representation problem (0000 and 1111), complicating equality test logic.
To store numbers with fractional parts, a three-field structure defined by the IEEE 754 standard is used:
1. Sign (1 bit): Defines the number's polarity.
2. Exponent (8 or 11 bits): Stored as "biased." You add 127 (for FP32) or 1023 (for FP64) to the actual exponent to avoid using internal sign bits.
3. Mantissa: Represents the significant digits of the normalized number. Noverflow implicitly handles the hidden bit to guarantee the exact binary result stored in memory.