The paper discuss the design of 1-bit full adder circuit using Shannon theorem. This proposed full adder circuit is used as one of the circuit component for implementation of Non- Restoring and Restoring divider circuits. The proposed adder and divider schematics are designed by using DSCH2 CAD tool and their layouts are generated by Microwind 3 VLSI CAD tool. The divider circuits are designed by using standard CMOS 0.35 microm feature size and corresponding power supply 3.5 V. The parameters analyses are carried out by BSIM 4 analysis. We have compared the simulated results of the Shannon based divider circuit with CPL and CMOS adder cell based divider circuits. We have further compared the results with published results and observed that the proposed adder cell based divider circuit dissipates lower power, gives faster response, lower latency, low EPI and high throughput.