The paper presents a digital adaptive (self-tuning) SISO controller within the delta model formulation. Some important advantages of the delta approach have been demonstrated in the context of parameter estimation as well as control design. The resultant self-tuner consists of a recursive identification procedure and a pole-placement design formulated via Diophantine equations. Adaptive control of a continuous stirred tank reactor (CSTR) is presented to show the performance and qualities of the proposed scheme.