Digital filters and signal processors when realized in hardware often use serial transfer of data. Multipliers which are capable of accepting variable coefficients and data in sign and magnitude notation and producing serial products of the same length as the input data word have been known for some time. This concise paper addresses the design of multipliers capable of accepting data in 2's complement notation, or both data and coefficients in 2's complement notation. It also considers multiplier recoding techniques, such as the Booth algorithm. Specialized (fixed coefficient) multiplier designs are considered briefly. Finally, multiplier rounding and overflow characteristics are discussed, and a rough comparison is made between the complexity of the various designs.