Assignment 9, due Apr 8

Always, on every assignment, please write your name legibly as it appears on your University ID and on the class list! All assignments will be due at the start of class on the day indicated, and unless there is what insurance companies call "an act of God" - something outside your control; the only exceptions to this rule will be by advance arrangement.

1. Consider this bit pattern: 01010101 (a total of 8 bits). Consider the above pattern in each of the following number formats. For each, give the corresponding decimal value (expressed as a fixed point decimal numbere) that the above pattern represents.

   a) Fixed point binary, with 4 places left of the point, and 4 places right of the point.

   b) Floating point, where the leftmost bit is the sign of the signed magnitude mantissa, the next 3 bits are the exponent, expressed as a biased binary number, and the rightmost 4 bits are the magnitude of the mantissa, a fixed-point binary number with the point immediately to the left of the most significant bit.

   c) Floating point, where the leftmost 4 bits are the two's complement integer exponent and the rightmost 4 bits are the two's complement fixed-point mantissa, with the point directly to the right of the sign bit.

2. Give the constant 1.0 (decimal) in each of the representations mentioned above. It need not be normalized.

3. In which of the above representations is normalization an issue, and in each representation where normalization is an issue, is the number given in problem 1 normalized, and is your answer to problem 2 normalized?