# Efficient Design of Reversible Adder and Multiplier Using Peres Gates
## 4 Schematic Representation  
A schematic diagram visually represents the connections between Peres gates, input bits (A, B), carry-ins, carry-outs, and the sum bits in the cascading arrangement of information preservation. This design methodology forms the foundation for the subsequent sections, where a detailed schematic representation, simulation results, and analysis will be presented to validate the functionality and performance of the proposed adders using Peres gates. Schematic diagrams illustrate the connections between Peres gates, input bits, and carry-outs at each stage, as depicted in Figures 7 and 8, representing the 2-bit Vedic multiplier and its 4-level decomposition, respectively. The reversible nature of Peres gates allows for a coherent design that ensures the reversibility of the overall circuit. Peres gates highlight the systematic application of reversible XOR operations at each stage, ensuring the overall circuit adheres to the principles of reversible logic. Figures 9-13 represent the generalized full adder, 1-bit full adder block schematic, 1-bit full adder using Peres gates, 1-bit adder quantum circuit using Peres gates, generalized block schematic of the n-bit ripple carry adder, and simplified block schematic of the n-bit ripple carry adder, respectively. Figure 5: Two-bit multiplier quantum circuit using Peres gates. Figure 6: Four-level decomposition of this two-bit multiplier. Figure 8: Four-level decomposition of this 2-bit Vedic multiplier. Figure 10: One-bit adder block schematic using Peres gates. Figure 7: Two-bit Vedic multiplier quantum circuit using Peres gates. Figure 9: Full Adder using two Peres gates. The use of Peres gates in this design methodology not only ensures reversibility but also opens the door to potential applications in quantum computing due to their inherent characteristics. A schematic diagram illustrates the connections between Peres gates, input bits, and carry-outs at each stage, as depicted in Figures 6 and 7. The reversible nature of Peres gates allows for a coherent design that ensures the reversibility of the overall circuit. The schematic representation visually captures the interconnection of Peres gates, input bits (A, B), carry-ins (Cin), and carry-outs (Cout) at each stage of the adders. The design utilizes Peres gates for reversible operations, ensuring information conservation throughout the addition process. The connections illustrate the systematic application of Peres gates, where each gate performs a reversible XOR operation on the corresponding bits of the input numbers and the carry-out from the previous stage. The final sum bits (S [n:0]) and carry out (Cout) collectively form the output of the full adders. The cascading arrangement of Peres gates signifies the stepwise progression through the bits of the input numbers, ensuring a coherent and reversible addition process. The external control lines represent the controlled-NOT operation applied by the Peres gates based on input bits. The proposed ripple carry adder (RCA) design utilizing Peres gates has been subjected to rigorous simulation to evaluate its functionality and performance for different configurations as 4-bit, 8-bit, and 16-bit addition and subtraction are shown in Figures 14-18. The analysis encompasses key aspects such as speed, quantum cost, and adhering to the principles of reversible logic. Figures 14-18 represent the 4-bit subtractors  
Figure 11: One-bit adder quantum circuit using Peres gates. Figure 12: Generalized block schematic representation of an n-bit ripple carry adder. Figure 13: Block schematic representation of an n-bit ripple carry adder using Peres gates. with outputs difference and borrows, 4-bit adder cum subtractor, 4-bit adder, 8-bit adder, and 16-bit adders, respectively, using Peres gates. The level-wise decomposition of the 4-bit multiplier is shown in Figure 19.  
Figure 6:0 Four-bit subtractor using Peres gates. Figure 6:1 Four-bit adder cum subtractor using Peres Gates. Figure 6:2 Four-bit adder using Peres gates.