Binary number of remainders (including the final quotient of one) forms the binary value, as each remainder must be either zero or one when dividing by two. For example, (357) is expressed as (101100101) Conversion from base-2 to base-10 simply inverts the preceding algorithm. The bits of the binary number are used one by one, starting with the most significant (leftmost) bit. Beginning with the value 0, the prior value is doubled, and the next bit is then added to produce the next value. This can be organized in a multi-column table. For example, to convert 10010101101 to decimal: The result is
Redundant binary representation time proportional to log("n") (where "n" is the number of digit) compared to a constant-time in two's complement. It is, however, possible to "partially" convert only the least-significant portion of a redundantly represented number to non-redundant form. This allows operations such as masking off the low "k" bits can be done in log("k") time. Redundant binary representation 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