In today’s Integrated Circuits (ICs), Built-In Self-Test (BIST) is becoming increasingly important as designs become more complicated. BIST is a design technique that allows a circuit to test itself Test Pattern Generator (TPG) using Linear Feedback Shift Resister (LFSR) is proposed which is more suitable for BIST architecture. In this paper, the authors have design ALU (Arithmetic and Logic Unit) in VHDL with BIST capability and compared the area overhead of with and without BIST.