Offset binary

Offset binary, also referred to as excess-K, excess-N, excess-e, excess code or biased representation, is a method for signed number representation where a signed number n is represented by the bit pattern corresponding to the unsigned number n+K, K being the biasing value or offset. There is no standard for offset binary, but most often the K for an n-bit binary word is K = 2n−1 (for example, the offset for a four-digit binary number would be 23=8). This has the consequence that the minimal negative value is represented by all-zeros, the "zero" value is represented by a 1 in the most significant bit and zero in all other bits, and the maximal positive value is represented by all-ones (conveniently, this is the same as using two's complement but with the most significant bit inverted). It also has the consequence that in a logical comparison operation, one gets the same result as with a true form numerical comparison operation, whereas, in two's complement notation a logical comparison will agree with true form numerical comparison operation if and only if the numbers being compared have the same sign. Otherwise the sense of the comparison will be inverted, with all negative values being taken as being larger than all positive values. The 5-bit Baudot code used in early synchronous multiplexing telegraphs can be seen as an offset-1 (excess-1) reflected binary (Gray) code. One historically prominent example of offset-64 (excess-64) notation was in the floating point (exponential) notation in the IBM System/360 and System/370 generations of computers. The "characteristic" (exponent) took the form of a seven-bit excess-64 number (The high-order bit of the same byte contained the sign of the significand). The 8-bit exponent in Microsoft Binary Format, a floating point format used in various programming languages (in particular BASIC) in the 1970s and 1980s, was encoded using an offset-129 notation (excess-129). The IEEE Standard for Floating-Point Arithmetic (IEEE 754) uses offset notation for the exponent part in each of its various formats of precision.