A method for changing numerals in certain nondecimal bases to numerals in other certain nondecimal bases, directly

Abstract

In “Numeration Systems for the Whole Numbers,” Booklet Number 3 of the NCTM's Topics in Mathematics for Elementary School Teachers (1964), on pages 22 through 25, a method is given for converting numerals in the binary system into numerals in the octal system of numeration by dividing the binary numeral into groups of three digits, beginning at the right and counting toward the left. Each group of three digits in the binary system is then made to correspond to a digit in the octal system. For example, the binary numeral 1110101 is used and divided into groups of three digits, thusly: 1-110-101. The 1 in the first left-band group equals one in the octal system. The 110 in the second group equals six in the octal system, and the 101 in the last group equals five in the octal system. A conversion table will more clearly show why this is so. (See Table 1.) Zeroes are prefixed to binary numerals 0, 1, 10, and 11 so that if these occur in other than the first left-hand group, one will know how to read them in the conversion process.