A hypothetical machine uses a floating$-$point storage scheme with $11$ binary $($base$-2)$ bits. The first and second bit hold the sign of the number and the sign of the exponent, respectively. The next $4$ bits hold the magnitude of the exponent. The final $5$ bits hold the mantissa.

a$)$ We would like to store the value $4400,$ but it cannot be exactly represented by the system. The value is roundedoff and stored as: $00110110001.$ What is the resulting normalized round$-$off error?

b$)$ What is the maximum normalized round$-$off error of the system. Assume rounding is employed.