2. Modify IEEE Standard 754 so that (1) the range of values that can be represented is increased by 8 times, (2) the precision of the represented values is decreased by 16 times, and (3) the single- and double-precision formats remain 32 bits and 64 bits, respectively. State the sizes of the three fields of your new representation and describe the encoding used for each field.

3. Two unsigned integers are added by a circuit that accepts J-bit operands. The carry out from the MSB is ignored; the J sum bits are examined. Consider the set of all pairs of operands (order does not matter because unsigned integer addition is commutative). There is a sum that can be produced by at least three distinct pairs of operands. Name such a sum and three operand pairs that have that sum.