Single Precision

A single precision number consists of the following.

• One bit to represent the sign (0 for positive and 1 for negative).
• Eight bits to represent the biased exponent (e). The exponent is biased by 127. That is, e = p + 127, where p is the exponent.
• Twenty-three bits to represent the magnitude of the fractional part (f) of the significand. (It is implied that this represents 1.f)

Therefore, the string 0 0000 1110 1010 0000 0000 0000 0000 000, as a single precision number, represents a positive number (0 as leading bit), with exponent 0000 1110 - 0111 111 = - 0111 0001, and significand 1.1010 0000 0000 0000 0000 000. So, this number is or (base 10).

Please verify that the smallest single precision positive number is and the largest single precision positive number is .