Explain floating point representation?

Floating point representation stores a real number using a sign, a power of 2 and a fraction, like scientific notation. A number is written as $(-1)^s \times 1.f \times 2^{e}$.

It has three fields: the sign bit $s$, the biased exponent $E = e + \text{bias}$, and the fraction (mantissa) $f$. In IEEE 754 single precision, 32 bits are split as 1, 8 and 23, with bias 127. Moving the binary point changes the exponent, so the same bits can hold very large and very small numbers. For example, $6.5 = 1.101_2 \times 2^2$.