Final answer:
The bias for single precision floating-point numbers is 127, while for double precision it is 1023. The bias is chosen as one less than the maximum value for an n-bit exponent field, enabling representation of positive and negative exponents.
Step-by-step explanation:
The bias for a floating-point number in single precision (IEEE 754 standard) is 127. This means that the exponent is stored with an offset of 127. For a double precision floating-point number, the bias is 1023. The bias is chosen such that it is one less than the maximum value for an n-bit exponent field with all bits set to 1, which is 2n-1 - 1.
For instance, single precision floating-point numbers have an 8-bit exponent field. Therefore, the bias for this field is 28-1 - 1, which is 127. Double precision floating-point numbers, on the other hand, have an 11-bit exponent field, leading to a bias of 211-1 - 1, which is 1023. The bias allows the representation of both positive and negative exponents and simplifies the arithmetic of floating-point operations.