Consider a 32-bit floating-point number with a sign bit in bit position 31, an 8-bit biased exponent in bit positions 30 to 23 and a 23-bit significand (mantissa) in bits 0 through 22. The exponent bias is 127 and the true exponent of -128 is never used. The significand (aka fraction or mantissa) is an absolute value (always positive) fraction less than one and there is no implied 1bit in the normalized form. The normalized form will hence be 0.1xxx...x.

(a) Give the dynamic range of the representation by expressing the smallest positive, largest positive, smallest negative, and largest negative numbers.

(b) Show the number 128.75 using the representation defined above.