A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, including two's complement, which use a single bit for each digit. Many of an RBR's properties differ from those of regular binary representation systems. Most importantly, an RBR allows addition without using a typical carry.[1] When compared to non-redundant representation, an RBR makes bitwise logical operation slower, but arithmetic operations are faster when a greater bit width is used.[2] Usually, each digit has its own sign that is not necessarily the same as the sign of the number represented. When digits have signs, that RBR is also a signed-digit representation.
^Phatak, Dhananjay S.; Koren, Israel (August 1994). "Hybrid Signed-Digit Number Systems: A Unified Framework for Redundant Number Representations with Bounded Carry Propagation Chains" (PDF). IEEE Transactions on Computers. 43 (8): 880–891. CiteSeerX 10.1.1.352.6407. doi:10.1109/12.295850.
^Lessard, Louis Philippe (2008). "Fast Arithmetic on FPGA Using Redundant Binary Apparatus". Retrieved 2015-09-12.
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