In recent years, reversible logic has emerged as a promising computing paradigm having its applications in low power computing, quantum computing, nanotechnology, optical computing and DNA computing. The classical set of gates such as AND, OR, and EXOR are not reversible. Recently, it was shown how to encode information in DNA and use DNA amplification to implement Fredkin gates. Furthermore, in the past Fredkin gates have been constructed using DNA, whose outputs are used as inputs for other Fredkin gates. Thus, it can be concluded that arbitrary circuits of Fredkin gates can be constructed using DNA. This has been the driving force leading to the design of reversible adder and multipliers using Fredkin gate. The ripple carry and carry skip adders designed from Fredkin gates already exist in literature; the present work provides an comprehensive extension and novelty to the existing work by introducing the reversible carry look-ahead adder and reversible multipliers using Fredkin gate. The reversible multipliers designed using Fredkin gates are array multiplier, Baugh Wooley multiplier and Wallace tree multiplier. Since, reversible 4:2 compressors are required for the design of reversible Wallace tree multiplier; hence 4:2 compressor is also designed with Fredkin gates. The reversible circuits designed and proposed in this paper form the basis of the ALU of a primitive DNA CPU.