A fictional machine uses a floating-point storage scheme. Each number is stored

Question

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

Explanation / Answer

1.
0105325   -->325*10^-5
0007767   -->767*10^7
1001846   -->846*10^1

2.
1100011000101011
= 1 * 2^0 = 1
1 * 2^1 = 2
0 * 2^2 = 0
1 * 2^3 = 8
0 * 2^4 = 0
1 * 2^5 = 32
0 * 2^6 = 0
0 * 2^7 = 0
0 * 2^8 = 0
1 * 2^9 = 512
1 * 2^10= 1024
0 * 2^11= 0
0 * 2^12= 0
0 * 2^13= 0
1 * 2^14= 16384
1 = Sign bit
-------------------
     -17936
-------------------

similarly 0110000111010110 = 25,046

3.             quo   remainder
   19 / 2 =   9          1
9/2    = 4    1
4/2    = 2    0
    2/2    =   1        0
    1/2   =     0         1
So
19 = 10011

Similarly
25 = 11001

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