A floating-point number system uses a 4-bit fraction and a 4-bit exponent with negative numbers expressed in 2’s complement. Design an efficient system that will multiply the number by -4 (minus four). Take all special cases into account and give a properly normalized result. Assume that the initial fraction is properly normalized or zero. This system multiplies only by -4. 

(a) Give examples of the normal and special cases that can occur (for multiplication by -4).
(b) Draw a block diagram of the system.
(c) Draw an SM chart for the control unit. Define all signals used.