Sams Teach Yourself C++ in 21 Days

In this example, the 4 in the third column represents the decimal value 196, and the 4 in

the first column represents the value 4. 196+4 = 200. Thus, 404 7 = 200 10.

Try another example. Convert the number 968 to base 6:

Column 54321

Power 64 63 62 61 60

Value 1296 216 36 6 1

Be certain you are comfortable with why these are the column values. Remember that

63 = 6*6*6 = 216.

To determine the base 6 representation of 968, you start at column 5. How many 1296s

are there in 968? There are none, so column 5 has 0. Dividing 968 by 216 yields 4 with a

remainder of 104. Column 4 is 4. That is, column 4 represents 4*216 (864).

You must now represent the remaining value (968-864 = 104). Dividing 104 by 36 yields

2 with a remainder of 32. Column 3 is 2. Dividing 32 by 6 yields 5 with a remainder of

2. The answer therefore is 4252 6.
   Column 54321
   Power 64 63 62 61 60
   Value 1296 216 36 6 1
   968 in 04252
   base 6
   Decimal 0 4216=864 236=72 56=30 21=2
   value

864+72+30+2 = 968.

Binary ............................................................................................................

Base 2 is the ultimate extension of this idea. In base 2, also called binary, there are only

two digits: 0 and 1. The columns are

Column 87654321

Power 27 26 25 24 23 22 21 20

Value 1286432168421

To convert the number 88 to base 2, you follow the same procedure: There are no 128s,

so column 8 is 0.

810 Appendix A

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