Subjects computer science

Floating Point Conversion 6185F1

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1. Let's clarify the problem: converting a floating-point binary number to its denary (decimal) equivalent involves understanding the mantissa and exponent. 2. The floating-point number is generally represented as $(-1)^s \times 1.m \times 2^{e - bias}$, where $s$ is the sign bit, $m$ is the mantissa (fractional part), and $e$ is the exponent. 3. The mantissa is a binary fraction, so to convert it to decimal, sum the values of each bit multiplied by $2^{-n}$ where $n$ is the bit position after the binary point. 4. For example, if the mantissa bits are $101$, the decimal equivalent is $1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = 0.5 + 0 + 0.125 = 0.625$. 5. The entire floating-point number is then calculated by applying the sign and exponent: $(-1)^s \times (1 + \text{mantissa decimal}) \times 2^{e - bias}$. 6. Remember to add the implicit leading 1 to the mantissa before conversion unless dealing with denormalized numbers. 7. This method ensures accurate conversion from binary floating-point to decimal.