octal digits = 2 4 5 . 3 7 . - - - - - - weight = 6 8 1 1 1 (in decimal 4 / / notation) 8 6 . 4The decimal value of each octal place-weight times its respective cipher multiplier can be determined as follows:
(2 x 6410) + (4 x 810) + (5 x 110) + (3 x 0.12510) + (7 x 0.01562510) = 165.48437510The technique for converting hexadecimal notation to decimal is the same, except that each successive place-weight changes by a factor of sixteen. Simply denote each digit’s weight, multiply each hexadecimal digit value by its respective weight (in decimal form), then add up all the decimal values to get a total. For example, the hexadecimal number 30F.A916 can be converted like this:
hexadecimal digits = 3 0 F . A 9 . - - - - - - weight = 2 1 1 1 1 (in decimal 5 6 / / notation) 6 1 2 . 6 5 . 6
(3 x 25610) + (0 x 1610) + (15 x 110) + (10 x 0.062510) + (9 x 0.0039062510) = 783.6601562510These basic techniques may be used to convert a numerical notation of any base into decimal form, if you know the value of that numeration system’s base.
by Majeed Ahmad
by Gary Elinoff
by Gary Elinoff