1. ## Floating point manipulation

I am having trouble understanding the mantissa of a floating point number. I have divided up the floating point number into the sign bit, the exponent and the mantissa, I have found the exponent, but I am not sure what to do with the mantissa? From what I have gathered so far i divide the mantissa by ten until I get a number between 1 and 10. after that i convert the number into a decimal with everything after the decimal point (or radix) being a fractional number. But when I do that on paper I dont get my intended number. How do i put the exponent and mantissa together to make a decimal from my floating point?

ex. input is 00111010000111111111011000001000
sign is 0
exponent is 01110100 which is 64+32+16+4-127=-11
mantissa is
00111111111011000001000 which would be 1.11111111011000001
when i convert that i get 1.99756622314 i dont know what to do with the -11 exponent and the answer i want is 6.1e-4

`mantissa is 00111111111011000001000 which would be 1.11111111011000001`