In this paper, we present a new mathematical analysis and implementation of block-least-mean-square (BLMS) for finite-impulse-response (FIR) adaptive filter using offset binary coding (OBC). The proposed approach is based on distributed arithmetic (DA) in which OBC combination of input samples are stored in look-up-table (LUT). The filter output and weight adaptation terms are computed by successive shift-and-accumulation (SA) of LUT contents. The recursive use of OBC scheme have reduced the complexity of LUT. Also, we suggested new structure for LUT update unit which involve fewer adders. In addition, a new SA unit is proposed to include the offset term in OBC representation of weights and error signals. Application Specific Integrated Circuit (ASIC) synthesis results show that the proposed scheme utilizes 51.73% less area, consumes 48.32% less power, provides nearly 2.33 times higher throughput for 32nd order filter with block length of 4 over the best existing scheme.