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Number Bases: Base 4 and Base 7 (page 2 of 3) Sections: Introduction & binary numbers, Base 4 & base 7, Octal & hexadecimal In base four, each digit in a number represents the number of copies of that power of four. That is, the first digit tells you how many ones you have; the second tells you how many fours you have; the third tells you how many sixteens (fourtimesfours) you have; the fourth tells you how many sixtyfours (fourtimesfourtimesfours) you have; and so on. The methodology for conversion between decimal and basefour numbers is just like that for converting between decimals and binaries, except that binary digits can be only "0" or "1", while the digits for basefour numbers can be "0", "1", "2", or "3". (As you might expect, there is no single solitary digit in basefour math that represents the quantity "four".)
I will do the same division that I did before, keeping track of the remainders. (You may want to use scratch paper for this.)
Then 357_{10} converts to 11211_{4}.
Note: Once I got "3" on top, I had to stop, because four cannot divide into 3. Reading the numbers off the division, I get that 807_{10} converts to 30213_{4}.
I will list out the digits, and then number them from the RIGHT, starting at zero:
Each digit stands for the number of copies I need for that power of four: 3×4^{4}
+ 0×4^{3} + 2×4^{2} + 1×4^{1} +
3×4^{0}
As expected, 30213_{4} converts to 807_{10}. Base Seven I can't think of any particular use for baseseven numbers, but they will serve us by providing some more practice with conversions. Copyright © Elizabeth Stapel 20012011 All Rights Reserved
I do the division: Then 357_{10} = 1020_{7}.
Then 13346_{10} = 53624_{7}.
I will list the digits, and count them off from the RIGHT, starting at zero:
Then I'll do the multiplication and addition: 5×7^{4}
+ 3×7^{3} + 6×7^{2} + 2×7^{1} +
4×7^{0}
^{} =
5×2401 + 3×343 + 6×49 + 2×7 + 4×1
Then 53624_{7} = 13346_{10}. << Previous Top  1  2  3  Return to Index Next >>



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