Silicon photonics is achieving developments in optical computing and information processing. It necessitates the efficient design of Arithmetic Logic Unit (ALU) to perform optical micro-operations such as adder/subtractor, comparator. The earlier work reported for ALU design used Mach-Zehnder Interferometer (MZI), semiconductor optical amplifiers, terahertz optical asymmetric demultiplexer (TOAD) and beam splitter. These approaches make optical circuit larger in size and difficult to integrate with Very Large Scale Integrated Optics (VLSIO). Here, we propose an all-optical ALU exclusively using Micro-Ring Resonator (MRR) to perform addition and comparison. The use of MRR to design ALU makes the proposed design novel and easy to integrate with VLSIO. The operations performed are one-bit addition and one-bit comparison. Beam splitter is replaced by MRR which has resulted in low intensity losses. The performance of the proposed ALU is discussed with simulation results and calculated losses. The output is verified for different input combinations of the half adder and comparator with electric field intensity distribution using 1550 nm wavelength. More losses are observed in comparator circuit as compared to adder circuit. Low losses and less MRR makes ALU design optimized.