A 54×54 bit multiplier with a new Redundant Binary Booth´s encoding

A fast multiplier with a new Redundant Binary Booth´s Encoding (RBBE) for Radix-8 has been developed. The new RBBE enables one to directly generate all Redundant Binary Partial Products (PP) including the hard multiple of 3×Multiplicand with no additional circuitry or time delay. Also, the use of TGs in Partial Product Selection Circuit permits the rapid generation of PPs. In this work, a word size of 54 bits is chosen to comply with the IEEE double-precision floating-point standard, which consists of one sign bit and 53 bits of fraction. Thus, the RBBE unit for Radix-8 generates 18 Redundant Binary PPs to be accumulated by a Redundant Binary Adder (RBA) tree. Due to the simplicity of the necessary interconnections between the adders, the RBA tree has a regular layout. The output of the RBA tree is in the Redundant Binary (RB) form, which needs to be converted to Standard Binary (SB) form. Although this conversion can be performed by a Carry Look Ahead (CLA) adder, a better conversion circuit has been designed to take advantage of the RB number system. The proposed design contains a converter of a higher speed and a lower transistor count. As a result, the proposed fast multiplier accepts two 54 bit SB numbers and produces a final product of 108 bit SB number.