1. Let's clarify the difference between fixed-point and floating-point binary representations. 2. In fixed-point binary, the position of the binary point is fixed, so the number is represented as an integer scaled by a fixed factor. 3. In floating-point binary, numbers are represented in the form $$\pm 1.m \times 2^{e}$$ where $m$ is the mantissa (or significand) and $e$ is the exponent. 4. The mantissa in floating-point is not a fixed-point number; it represents the significant digits of the number normalized to be between 1 and 2 (for normalized numbers). 5. The exponent shifts the binary point, allowing representation of very large or very small numbers. 6. Treating the mantissa as a fixed-point binary number ignores the exponent's role and the normalization, which is why it misses the point of floating-point representation. 7. To correctly interpret a floating-point number, you must combine the mantissa and exponent as $$\text{value} = (-1)^{\text{sign}} \times (1 + \text{mantissa fraction}) \times 2^{\text{exponent} - \text{bias}}$$ where the bias depends on the floating-point format (e.g., 127 for IEEE 754 single precision).