Discuss biasing with reference to floating point representation.

Biasing means adding a fixed constant, called the bias, to the true exponent before storing it. The stored value is then always a positive (unsigned) number, so no sign bit is needed for the exponent. It also lets us compare two floating point numbers using plain integer comparison.

In IEEE 754 single precision the bias is 127, so $E = e + 127$. In double precision the bias is 1023. For example, a true exponent of $-3$ is stored as $-3 + 127 = 124$, and a true exponent of $5$ is stored as $132$.