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MATHEMATICS CONCEPTS

Numeration systems


Addition and Multiplication in base b

Multiplication in any base is related to addition, for mulitplication is essentially repeated addition.

Addition
Addition in all bases is similar, except that binary addition is particularly simple. Consider binary addition.
 1011
 +101
-------
10000
Check: 10112, 1012, and 100002 are 11, 5, and 16, respectively, in the decimal system. In adding, a "CARRY" results if there are two or more 1's in a vertical column. This is due to the binary rule 1+1=10.

Multiplication
Consider binary multiplication.
    1011
   X 111
-------------
    1011
  1011
 1011
-------------
1001101

Here is a multiplication in base 5
   342
  X 43
---------
  2131
3023
----------
32411
Check: 3425, 435, and 324115 are 97, 23, and 2231, respectively, in the decimal system.

(G.R.T.)

>> Subtraction and Division in base b

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