High-level trial and error method is a method to convert multi-level division into intra-table division according to the high-level digits in divisor and the dividend to be divided, and determine the number of quotient digits in turn by using multiplication formula.
In division operation and trial quotient, divisor plays a leading role. Trial quotient of division and multiplication formula in table. Divider is the division of single digits, which is converted into division calculation in the table, and the quotient is tried by multiplication formula. The principle of one-digit division calculation is to convert one-digit division into several in-table division calculations. In-table division and one-digit division, the method of trying quotient with multiplication formula should be called multiplication formula trying commercial law.
The divider is a multi-digit division, which is not converted into an in-table division and is not calculated according to the in-table division. The quotient is tried by the multiplication formula. In fact, it is possible, that is to say, the principle of multi-digit division is the same as that of single-digit division, and the quotient can also be tried by multiplication formula. Because the counting follows the principle of bit value, the counting unit of high order and its number is large, which plays a major role in determining the numerical value, while the counting unit of low order and its number is small, which has little effect on determining the numerical value. The low figures are all zeros after rounding, which only takes up digits. Therefore, in the trial quotient of multi-digit division, the divisor and its low digits can be ignored, and only the digits on the highest digit after rounding can participate in the trial quotient. The product of it and the quotient of each trial is one or two digits, so the divisor only needs the first digit or the first two digits of the divided part in each trial. At this time, the divisor and the number of bits to be divided and the reduction rate are the same. According to the nature of quotient, as long as the high digits of divisor match the high digits of dividend, multi-digit division can determine the number on the corresponding digits of quotient. In this way, no matter how many divisors there are, division can be converted into division in the table and calculated according to the division in the table, which creates conditions for trial quotient with multiplication formula.