exponentbits

Exponentbits refers to the number of bits allocated to the exponent field in a floating-point representation. In most modern formats, a floating-point number is divided into three parts: a sign bit, an exponent field, and a significand (mantissa). The exponentbits determine how large or small the representable values can be by encoding the exponent in a biased form.

The exponent is stored with a bias to allow both positive and negative exponents. For a format with k exponent bits, the bias is usually 2^(k-1) − 1. The range of representable exponents, together with the significand, sets the practical range of values: larger exponentbits increase the range and reduce the likelihood of underflow or overflow, but they also reduce the available bits for precision if the total width is fixed.

Common examples include IEEE 754 formats: single precision uses 8 exponent bits, bias 127, and 23 significand bits; double precision uses 11 exponent bits, bias 1023, and 52 significand bits. Half precision uses 5 exponent bits, bias 15, and 10 significand bits. Some formats like bfloat16 use 8 exponent bits but a smaller significand, trading precision for range compatibility with 32-bit floats.

Special values arise from certain exponent patterns: an all-zero exponent typically denotes subnormals or zero, while an all-ones exponent denotes infinities and NaNs depending on the significand. Exponentbits, therefore, are central to a floating-point format’s range, distribution of representable numbers, and handling of exceptional values.