Working with Numbers: Binary and Hexadecimal 809A
That is, eight asterisks and seven. That would be represented in base 8 as 17 8. That is,
one eight and seven ones.Converting to Different Bases ............................................................................
You can represent the number fifteen in base 10 as 15, in base 9 as 16 9 , in base 8 as 17 8 ,
in base 7 as 21 7. Why 21 7? In base 7, there is no numeral 8. To represent fifteen, you
need two sevens and one 1.
How do you generalize the process? To convert a base 10 number to base 7, think about
the columns: In base 7 they are ones, sevens, forty-nines, three-hundred forty-threes, and
so on. Why these columns? They represent 7^0 ,7^1 ,7^2 ,7^4 , and so forth.
Remember, any number to the 0th power (for example, 7^0 ) is 1, any number to the first
power (for example, 7^1 ) is the number itself, any number to the second power is that
number times itself (7^2 = 7*7 = 49), and any number to the third power is that number
times itself and then times itself again (7^3 = 7*7*7 = 343).
Create a table for yourself:
Column 4321
Power 73 72 71 70
Value 343 49 7 1The first row represents the column number. The second row represents the power of 7.
The third row represents the decimal value of each number in that row.
To convert from a decimal value to base 7, here is the procedure: Examine the number
and decide which column to use first. If the number is 200, for example, you know that
column 4 (343) is 0, and you don’t have to worry about it.
To find out how many 49s there are, divide 200 by 49. The answer is 4, so put 4 in col-
umn 3 and examine the remainder: 4. There are no 7s in 4, so put a zero in the 7s col-
umn. There are 4 ones in 4, so put a 4 in the 1s column. The answer is 404 7.
Column 4321
Power 73 72 71 70
Value 343 49 7 1
200 in base 7 0404
Decimal value 0 4*49 = 196 0 4*1 = 429 0672327112_app_a.qxd 11/19/04 12:30 PM Page 809