Why does a float variable stop incrementing at number ‘16777216’ in the following C# code?
float a = 0 ;
while (true)
{
a++;
if (a > 16777216)
break;
}
a) Sign and Exponent for ‘16777217’ is same as for ‘16777216’
b) Mantissa is different for ‘16777216’ and ‘16777217’
c) Sign and Exponent for ‘16777217’ is different from ‘16777216’
d) None of the mentioned

Answer: b
Explanation: 16777216 is exactly 224, and would be represented as 32-bit float like so:
sign = 0 (positive number)
exponent = 24 (stored as 24 + 127 = 151 = 10010111)
mantissa = . 0
As 32 bits floating-point representation: 0 10010111 00000000000000000000000
Therefore: Value = (+ 1) * 2 ^ 24 * (1. 0 + . 0) = 2 ^ 24 = 16777216
Now let’s look at the number 16777217, or exactly 224 + 1: sign and exponent are the same. Mantissa should have to be exactly 2-24 so that (+ 1) * 2 ^ 24 * (1. 0 + 2 ^-24) = 2 ^ 24 + 1 = 16777217 and here lies the actual problem. The mantissa cannot have the value 2-24 because it only has 23 bits, so the number 16777217 just cannot be represented with the accuracy of 32-bit floating points numbers.