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Now let's define range which a normalised mantissa can signify. Let's presume that our present representations has normalised mantissa so left most bit can't be zero so it has to be 1. So it's not required to store this first bit and it's being presumed implicitly for number. So a 23-bit mantissa can signify 23 + 1 = 24 bit mantissa in our representation.
So smallest mantissa value can be:
Implicit first bit as 1 followed by 23 zero's which is
0.1000 0000 0000 0000 0000 0000
Decimal equivalent = 1 × 2-1 = 0.5
Maximum value of mantissa:
Implicit first bit 1 followed by 23 one's which is
0.1111 1111 1111 1111 1111 1111
Decimal equivalent:
For finding binary correspondent let's add 2-24 to above mantissa as below
Binary: 0.1111 1111 1111 1111 1111 1111
Mutation: However it may appear that the above recombinations are a little arbitrary that especially as points defining whether crossover and inversion occur are chosen random
Convert binary number in two's compliment form 0100 1000. Converting the binary number into 2's compliment from 0100 1000 is given below: 01001000 => 10111000
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