Decimal and, only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called "decimal fractions" or "decimal numbers" for forming the "decimal numeral system". For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−". The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the decimal separator is the dot "" in many countries (including English speaking ones),
Binary integer decimal encoding, it is encoded as a series of "p" decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal (BID) encoding, it is encoded as a binary number. Using the fact that 2 = 1024 is only slightly more than 10 = 1000, 3"n"-digit decimal numbers can be efficiently packed into 10"n" binary bits. However, the IEEE formats have significands of 3"n"+1 digits, which would generally require 10"n"+4 binary bits to represent. This would not be efficient, because only 10 of