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2.1 Conversion to decimal. ... 0.6 0.5 0.4 0.3 0.2 0.1 0 ... the trit of the quotient must be 1 or T. If the dividend is between the plus and minus of half the ...
Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = 1585 / 1000 ); it may also be written as a ratio of the form k / 2 n ·5 m (e.g. 1.585 = 317 / 2 3 ·5 2 ).
If an unknown weight W is balanced with 3 (3 1) on its pan and 1 and 27 (3 0 and 3 3) on the other, then its weight in decimal is 25 or 10 1 1 in balanced base-3. 10 1 1 3 = 1 × 3 3 + 0 × 3 2 − 1 × 3 1 + 1 × 3 0 = 25.
A negative base (or negative radix) may be used to construct a non-standard positional numeral system.Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r (r ≥ 2).
For example, a Q15.1 format number requires 15+1 = 16 bits, has resolution 2 −1 = 0.5, and the representable values range from −2 14 = −16384.0 to +2 14 − 2 −1 = +16383.5. In hexadecimal, the negative values range from 0x8000 to 0xFFFF followed by the non-negative ones from 0x0000 to 0x7FFF.
Also, the prime factor 2 appears twice in the factorization of twelve, whereas only once in the factorization of ten; which means that most fractions whose denominators are powers of two will have a shorter, more convenient terminating representation in duodecimal than in decimal: 1/(2 2) = 0.25 10 = 0.3 12; 1/(2 3) = 0.125 10 = 0.16 12
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
However, a binary number system with base −2 is also possible. The rightmost bit represents (−2) 0 = +1, the next bit represents (−2) 1 = −2, the next bit (−2) 2 = +4 and so on, with alternating sign. The numbers that can be represented with four bits are shown in the comparison table below.