Final answer:
The floating-point representation with a 1-bit sign, 3-bit exponent, and 4-bit mantissa does not correspond to a standard IEEE 754 format. It's a simplified model for understanding how floating-point numbers are represented in binary. These numbers use scientific notation to ensure all significant figures are captured in the mantissa.
Step-by-step explanation:
The representation of a floating-point number with a 1-bit sign, 3-bit exponent, and 4-bit mantissa does not match any of the standard IEEE 754 formats, which are single precision, double precision, half precision, or quadruple precision. However, this question seems to be asking about a simplified or hypothetical floating-point format for educational purposes. In IEEE 754, floating-point numbers are represented using scientific notation in binary, which is similar to decimal scientific notation. For instance, in decimal, the number 0.0000045 is written in scientific notation as 4.5 × 10-6, ensuring that all significant figures are visible.
Similarly, binary scientific notation ensures the precision of the mantissa is explicit by normalizing the number so that the first digit is a 1 (after the radix point for binary). For example, the floating-point representation of the simplified 8-bit format described in the question would look like:
1-bit sign | 3-bit exponent | 4-bit mantissa
The sign bit indicates if the number is positive or negative, the exponent determines the scale of the number, and the mantissa provides the precision. Exponential notation in scientific terms is a powerful tool to express numbers accurately, ensuring that all significant figures are conveyed without ambiguity, just like in the binary floating-point representation.