Kvotientsiffer

Kvotientsiffer, or quotient digit, is the digit that appears at a given position in the base-b representation of a division’s result. In a division of two integers expressed in a positional numeral system, the quotient is obtained step by step, and each step yields one kvotientsiffer. In base-10 arithmetic, the quotient is written as q_k q_{k-1} ... q_0, and each q_i is a kvotientsiffer. The full quotient is reconstructed as Q = sum q_i b^i, where b is the base (10 in decimal).

In manual long division and in many division algorithms used in computing, the divisor is compared with the current partial dividend, and the number of times the divisor fits into that partial dividend is the kvotientsiffer for that step. In computer arithmetic, quotient digits are produced by algorithms that estimate and refine each digit, often with techniques to ensure that divisor times the digit does not exceed the partial dividend. Some methods generate digits from most significant to least significant, while others use parallel or iterative schemes with carry handling.

Example: 248 ÷ 8. Looking at the first partial dividend, 24, eight fits into 24 three times, so the first kvotientsiffer is 3 (and 8×3 = 24 is subtracted). Bring down the remaining 8; 8 ÷ 8 = 1, so the second kvotientsiffer is 1. The quotient is 31, with remainder 0.

Kvotientsiffer are fundamental in both manual calculation and digital division, serving as the building blocks of the final quotient in any base-n division.