Numerical Methods

A fictional machine uses a floating-point storage scheme. Each number is stored using 7 bits and base-10. The first bit holds the sign of the number, the next 3 hold the sign and magnitude of the exponent, and the final 3 bits store the mantissa. How will the following numbers be stored if the system uses a round half to even scheme? a) 0.003254 b) 7, 665,000,000 c) -8, 459 A system uses the signed magnitude method and 16 bits to store integers. Calculate the base-10 equivalents of the following stored integers: a) 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 b) 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 Write are the base-2 equivalents of the following base-10 numbers a) 19 b) 25