ECE-C490 Security in Computing Winter Term 2005 Quiz #2 Solutions Consider a hypothetical floating point system in radix 2 (binary) with the following characteristics: 1 sign bit 8 bits for a biased exponent 20 bits for the mantissa For this hypothetical system, find: The precision The range, and The maximum and minimum exponent. Explain all of your reasoning! Precision can be defined in one of two ways: the number of bits for the mantissa (20) or the smallest possible difference in magnitude between any two numbers represented by the system, which would be the magnitude that can be contributed by the least significant bit of the mantissa, or 2-20. Range is the range of numbers that can be represented by the system. Obviously the largest would be the positive number with the largest mantissa (all 1s) and the largest exponent (all 1s). The actual value of this number would be 1.(1 - 220) * 2128. The smallest number would have the same magnitude in the mantissa, but would be negative. Maximum and minimum exponent depend on the bias used for the exponent. Given 8 bits for the exponent, the bias would be 127. Thus we can represent exponents from –127 to +128.