C Programming - Floating Point Issues - Discussion

Why we multiply in 2?

5.375

5 --> 101.

0.375 * 2 = 0.75.
0.75 * 2 = 1.5.
0.5 * 2 = 1.0.

Therefore it will be,
5.375 -> 101.011.

If base of 5.375 is 10 then answer is 101.011 others answer is D.

101.011 converting to decimal.

= 1*(2^2)+0*(2^1)+1*(2^0).0*(2^-1)+1*(2^-2)+1*(2^-3).
= 4+0+1.0+(1/4)+(1/8).
= 5.375 Answer.

If equivalent is to use in binary formation.

By language is,

5<--1011011.
1010101.
101.1011.
1100110.
1011111.

So by doing this we'll get right formation.

5.375.
Here 5-> 101.

0.375*2 = 0.750 decimal part = 0.
(omit decimal part).

0.750*2 = 1.50 decimal part = 1.
(omit decimal part).

0.5*2 = 1.0 decimal part = 1.
So, the ans is 101.011 (011 from top to down).

5.375

5 --> 101.

0.375 * 2 = 0.75.
0.75 * 2 = 1.5.
0.5 * 2 = 1.0.

Consider decimals from top to bottom (0 1 1).

THEREFORE, 5.375=101.011.

5.375 is in decimal form.
5=101(In binary format).

Now we have to convert 0.375 into binary format as below.

0.375 * 2 = 0.750 ---> 0 (take the before .(dot) value .i.e Integer value).
0.750 * 2 = 1.500 ---> 1 (take the before .(dot) value .i.e Integer value).

*Note: if we got 1. Some value then remove the 1 value .i.e 0.500.

0.500 * 2 = 1.000 ---> 1 (take the before .(dot) value .i.e Integer value).

*Note: The above Process will be continue until we got fractional part will be getting 0(zero).

So,
0.375 = 011.

So,
5.375 = 101.011.

The binary of 5 = 101.
And,
Now for the binary 0.375*2=0.750----->0 |
0.750*2=1.500----->1 |
0.500*2=1.000------>1 |


For 0.375---> 011.

If equivalent is to use in binary formation.
by language is,

5<--1011011
1010101
101.1011
1100110.
1011111.

So by doing this we'll get right formation.