P
R TR G AR S

s o 23
iy e

4

et PP

e

 

2 et i i T b B S eV T L AT e N T R e N

58 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

Then, performing all our operations in the old notation,
ay’ is the remainder obtaind by dividing e by 7/, a,’ is the
remainder obtaind by dividing the quotient of that division
by #’, and so on.

Thus we compute as follows:

7 | 4398 (f)
2 628 Rems—2k—a,"
89 S =a
12 5 =a)
1 =iy
0 1=a

Hence 4398('f) = 15552(7).

Since we are accustomd to operate in the decimal system,
the third method is the shortest and easiest when we wish to
change from the decimal notation to another.

When we operate according to the first or the second method,
we practically use the third method to express the old base
and digits in the new notation, altho this work is usually so
simple that we perform it mentally.

Now let us change 15552(7), the result just obtaind, back
into the decimal notation.
By the first method,

15552(7) = 1 X T4+ 5 X B+5X 72 +5X 7+ 2
72 = 49('f) 1 X 7%= 2401(*?)
73 = 343 5% 73 = 1715
74 = 2401 5% 7= 245
5X7 = 35
2 = 2

15552(7) = 4398(*f)