The document describes designing and simulating half adder, full adder, half subtractor, and full subtractor circuits using logic gates in Cadence NC-SIM. A half adder adds two bits and produces a sum and carry output. A full adder adds three bits and produces a sum and carry output. A half subtractor subtracts one bit from another and produces a difference bit and borrow bit, while a full subtractor subtracts bits considering borrow from the next column and produces difference and borrow bits. The circuits are simulated and truth tables are verified. These circuits can be used to add and subtract binary numbers.