This standard not only specifies how floating-point numbers are to be represented, but also how arithmetic calculations on these numbers should be performed. ![]() The WB_FPU supports single precision (32-bit) binary floating-point numbers, formatted in accordance with the IEEE 754 Standard. Figure 1 shows the composition of a binary floating-point number under this standard.įigure 1. If this bit is '1', then the number is negative. If this bit is '0', then the number is positive. This base is implicit and is therefore not stored as part of the 32-bit format. To facilitate both positive and negative exponent values, a bias value is added to the actual exponent to arrive at the 8-bit value that gets stored. For IEEE 754 single precision floats, the bias value used is 127. The significand represents the precision bits of the number. The leading bit – to the left of the radix point – is required to be non-zero.The radix point is always placed after the first non-zero digit (e.g.Normalization leads to two important points: The WB_FPU supports normalized floating-point numbers. As we are using the binary system, this bit can only be 1. The significand therefore effectively has 24-bit resolution, but only 23 bits are used to represent the fractional part of the number only – the digits to the right of the radix point.Īs such, the leading bit is implicit and not stored as part of the significand. ![]() If the fractional part of the number (written in binary notation) is less than 23 bits, the remaining right-hand bits are padded with zeroes.
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