Rank the following operations according to:

(a) delay required to complete them assuming the operands are n bits long ( write the expression for the delay in terms of n using big O notation). Assume the delay of a standard 2 input NAND/NOR is 1 unit and a 2-input MUX and/or XOR/XNOR is 1 unit.

(b) Area required (each gate occupies roughly 1 unit of area)

The operations to be ranked are:

1. Check if a given number is zero

2. determine the parity of an operand(i.e. determine if the number of "1"'s in the binary representation of the operand is even or odd)

3. Addition of two numbers to produce an output in the redundant carry-save format.

4. Addition of two numbers to produce an output in the redundant signed-digit format where each digit is the range of [-1,1]

5. addition to produce non-redundant output