Nanoelectronics are electronic components that are often only a few nanometers in size. The field of nanoelectronics encompasses a wide range of products and materials that share the trait of being so small that physical forces can modify their characteristics on a nanoscale. These nanoscale devices are dominated by quantum processes including atomistic disorder and tunneling.In contrast to nanoelectronics, which involves the scaling down of devices to nanoscale levels, molecular electronics is concerned with electronic activities that take place within molecule structures. Detection of molecular conductance plays a vital role in the field of molecular electronics and nanotechnology. The ability to measure the conductive behavior of molecules is necessary to study their surface properties, defects, electronic structures, and for bio-sensing. To determine the conductance of the molecule, it is necessary to deduce the current passing through it. This is achieved by applying a voltage bias across the molecule and the detection instrument. Instruments like Scanning Tunneling Microscope (STM) and chip-based characterization (Probe Station) are used to fetch the amount of current flowing through the molecules. The current through molecules can be very small to measure and needs to be amplified. Linear amplifiers are widely used for amplifying these small currents, but due to their low dynamic range they are being replaced by logarithmic amplifiers. This thesis project aims to customize a logarithmic amplifier design to the interface with these instruments to measure the current flowing through these molecules. This thesis starts with a review of a linear- current amplifier-based technology that is used for measuring small currents and its challenges. It then introduces logarithmic amplifier for overcoming those obstacles. This thesis involves design, fabrication, and characterization of the built logarithmic amplifier. Furthermore, the setup includes a custom designed logarithmic amplifier that can be used with instruments like Scanning Tunneling Microscope (STM) and probe station. The key objective of the research is to accurately calibrate the logarithmic amplifier for measurement of currents over a wide range from picoamperes to milliamperes. Dummy resistors with different resistance values are used to replace the sample of which the conductance is to be measured, for testing and calibrating purposes. Bandwidth of the circuit is tested using these different values of resistors.