Can someone please help me with this following question please :) Consider a new
ID: 3869462 • Letter: C
Question
Can someone please help me with this following question please :)
Consider a new computer system which stores data in “quads”, i.e. it has four states 0, 1, 2 and 3 (as opposed to binary which has only two, 0 and 1). Now imagine that numbers are stored in an 8 quad format where there is one quad for the sign of the number, two quads for the exponent, another one quad for the sign of the exponent and four quads for the normalised mantissa.
Find:
i. The mantissa and exponent of the largest positive number that can be represented in this system.
ii. Now convert this number to a decimal number.
Explanation / Answer
(a) The largest exponent possible is
3334 = 3*42 + 3*4 + 3 = 63
The largest mantissa possible is 3333333.
0.33333334 = 0.9999390
Thus, the largest positive decimal number that can be represented is 0.9999390 x 463 = 8.507 x 1037
(b) The smallest exponent possible is -3334 = -63.
The smallest mantissa possible is 1000000.
0.14 = 0.25
Thus, the smallest positive decimal number that can be represented is 0.25 x 4-63 = 2.939 x 10-39.
(c) The machine epsilon is b-p/2 = 4-7/2 = 3.052 x 10-5.