Problem $4$: $(16$ marks$)$ Arithmetic for Digital Design $/$ Shift Register

$(3$ marks$)$ Design a decrementer using FA which is a circuit that subtracts $1$ from a fourbit binary number.

$(6$ marks$)$ Assume the following full adder,

a$.$ What is the function of carry propagate and carry generate?

Carry generate $=q,$

Carry propagate $=q,$

b$.$ Draw the circuit that performs a $4-$bit binary ripple addition.

c$.$ Indicate the critical path in the design.

$(3$ marks$)$ Show the steps to multiply B by $7$

$(4$ marks$)$ Draw the block diagram of a $2-$bit shift register with parallel load assuming the following:

Inputs: clock $CP,$ Loaded data $D_A,D_B,$ Control SHIFT, Serial Input IN Output: serial Output OUT

$3$