Reversible logic has received a great deal of attention from many researchers over recent years for its enormous potential for application in quantum computing and nanotechnology due to its ability to reduce power consumption, which is the main requirement in low power VLSI design. This article presents the new design of reversible arithmetic circuit and Logic unit. The designs in this article showcases reversible Adder/Subtractor based on Carry Look Ahead Logic and reversible logic unit that can perform four different operations. The arithmetic operations, include addition, subtraction and the logical operations, include AND, OR, NOT, and XOR. All modules have been designed using the basic and new reversible gates. The efficiency of the proposed design has been mentioned in terms of number of gates required, garbage outputs produced, number of constant inputs required, and quantum cost needed. The design of both the circuit is then further combined for reversible ALU.