Does anyone know how to represent normal numbers eg 16 and 100 in the normalised floating point in computing?

Question

Hiya, I am doing a BTEC IT Practitioners course at college and one of the questions which I am stuck on is representing numbers in computer arithmetic, the question which I am having difficulty on is:

Express the following decimal numbers:
(i) 16, (ii) 100.
in the normalized floating-point form m2e

If the following format is used for the binary representation:
Exponent e 4-bits, twos complement representation
Mantissa m 8-bits, sign-and magnitude convention
Write down the complete 12-bit binary pattern for each of the above numbers

Answer 1

16 = 1.6 x 10^1 (standard index form)

16 = .16 x 10^2 (normalised form)



Now do the same again but with the binary version.

16 = 10000 (b) = .10000 x 2^5 = .10000 x 2^101 (b)

The mantissa needs to be increased from 5 to 8 bits by adding trailing zeros. The exponent needs to be increased from 3 to 4 bits by adding a leading zero.

Result: 100000000101

Not too difficult with positive numbers.

Answer 2

performing some numerology, eh? there are various letter combos which will upload as much as a hundred. we are in a position to narrow it down slightly although. at the start, you won't be in a position to have better than 26 letters, by using fact even at its lowest (a string of 26 "a"s) this could upload as much as 26. Likewise, you are able to have a minimum of four letters, by using fact "zzz" could be seventy 8 which continues to be under a hundred. That a minimum of narrows it down slightly. As for paying for each and every of the examples it quite is a be conscious in english, you are able to actual could placed in writing and run some style of workstation software. you will get a dictionary record (a flat record that in simple terms has a catalogue of dictionary words), and write a loop that provides up the letters of each and every be conscious and writes the be conscious out if the result's a hundred. i've got written those in the previous. hire a command like "asc(x) - ninety six" that converts a letter to its numerical fee.

Answer 3

maybe you should ask for help from the professors if your having trouble. At least they can explain it, instead of just receiving the answer. What if this is on your finals?