Convert base-31 to base-14 Online | Free numbers Converter

31 Number System

The base-31 number system, also called the untrigesimal system, is a positional numeral system that uses thirty-one symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, and T, where A represents ten, B eleven, C twelve, D thirteen, E fourteen, F fifteen, G sixteen, H seventeen, I eighteen, J nineteen, K twenty, L twenty-one, M twenty-two, N twenty-three, O twenty-four, P twenty-five, Q twenty-six, R twenty-seven, S twenty-eight, and T twenty-nine in decimal. Each digit’s position represents a power of 31, starting from $31^0$ at the rightmost digit and increasing to the left. For example, the base-31 number 3T7 equals $3 \times 31^2 + 29 \times 31^1 + 7 \times 31^0 = 2883 + 899 + 7 = 3789$ in decimal. Base-31 is primarily used in theoretical mathematics, number theory, and educational exercises to explore alternative numeral systems, positional notation, and arithmetic patterns. Understanding base-31 allows learners to perform arithmetic operations, convert numbers between bases, and analyze properties of non-decimal systems. Although rarely used in computing or daily life, studying the untrigesimal system enhances logical reasoning, problem-solving skills, and comprehension of abstract number representations. It also provides a foundation for higher-level numeral systems and theoretical mathematics.

Number System

The base-14 number system, also called the tetradecimal system, is a positional numeral system that uses fourteen symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and D, where A represents ten, B eleven, C twelve, and D thirteen in decimal. Each digit’s position represents a power of 14, starting from $14^0$ at the rightmost digit and increasing to the left. For example, the base-14 number 3C5 equals $3 \times 14^2 + 12 \times 14^1 + 5 \times 14^0 = 588 + 168 + 5 = 761$ in decimal. Base-14 is primarily studied in mathematics and number theory to explore alternative numeral systems, positional notation, and arithmetic patterns beyond decimal. Understanding base-14 helps in performing arithmetic operations, converting between bases, and analyzing divisibility rules in non-decimal systems. Although it is not commonly used in computing or daily life, studying base-14 provides insights into the structure and flexibility of positional numeral systems. It also strengthens mathematical reasoning, problem-solving skills, and comprehension of abstract number systems. Base-14, like other higher bases, is valuable for theoretical exploration, coding theory, and educational exercises, helping learners understand how numbers can be represented efficiently in various numeral frameworks.