Final answer:
Single precision represents floating point numbers using 32 bits, whereas double precision uses 64 bits for higher accuracy. Overflow is when a result is too large to represent, and underflow is when it is too small, leading to values near zero or infinity.
Step-by-step explanation:
Single precision and double precision are two measures of accuracy in representing floating point numbers. In single precision, 32 bits are used to represent a floating point number, with 1 bit for the sign, 8 bits for the exponent, and 23 bits for the mantissa (or significant).
This format is limited in terms of range and precision. In contrast, double precision uses 64 bits in total, with 1 bit for the sign, 11 bits for the exponent, and 52 bits for the mantissa. As a result, it allows for a much larger range and higher precision, making it more appropriate for calculations that require a higher degree of accuracy.
Overflow occurs when a calculation produces a result that is too large to be represented within the range of the allowable exponent. This usually leads to the result being represented as infinity. On the other hand, underflow happens when the result of a computation is smaller than the smallest value that can be represented, resulting in a result close to zero. Both overflow and underflow can lead to significant errors in computations if not handled properly.