why do we need to use binary fixed width such as (_ _ _) _2,3 in the circuit?

Does this logic circuit implement the operation of taking the integer x represented in binary fixed- width 3 as (X2X1 Xo)2,3 and computing the following operations so that the result equals (y2yyo)2,3? If yes, explain why using the definition of binary fixed-width representation and consider all possible inputs. If no, provide specific example input values, trace the circuit (or use the input-output definition table) to compute its output for this example, and use the definition to calculate the two numbers being represented and explain why these numbers support your conclusion (a) x mod 8 (b) x div 4 Does this logic circuit implement the operation of taking the integer x represented in binary fixed- width 3 as (X2X1 Xo)2,3 and computing the following operations so that the result equals (y2yyo)2,3? If yes, explain why using the definition of binary fixed-width representation and consider all possible inputs. If no, provide specific example input values, trace the circuit (or use the input-output definition table) to compute its output for this example, and use the definition to calculate the two numbers being represented and explain why these numbers support your conclusion (a) x mod 8 (b) x div 4