Working in Base 7Date: 08/02/2007 at 07:12:00 From: Anne Subject: Could you please explain base 7 to me? How can I solve the four basic operations (addition, subtraction, multiplication and division) using base 7? Can you give me an example on the formula on how to do it? I tried solving and converting numbers to base 6 using blocks, but am still confused in using base 7. Date: 08/02/2007 at 08:41:53 From: Doctor Ian Subject: Re: Could you please explain base 7 to me? Hi Anne, The easiest way to see how it works is to do some operations in base 10 and base 7 side by side. For example, Base 10 Base 7 56 34 + 78 + 65 ---- ---- In base 10, we start with the units column, and add 6+8. That gives us 14, which is too large to represent with one digit. So we keep 4 of that, and carry a group of 10 over to the tens column: 1 56 34 + 78 + 65 ---- ---- 4 What about in base 7? It's the same thing: 4+5 gives us 9, which is too big to represent as a single digit in base 7 (because we have only the digits 0-6). In base 7, 9 is 12 (1*7 + 2), so we keep the 2 and carry a group of 7 over to the 'sevens' column: 1 1 56 34 + 78 + 65 ---- ---- 4 2 Now we move to the next column. In base 10, we add 5 and 7, plus the carry, to get 13. That's too big for a single digit, so we carry again: 11 1 56 34 + 78 + 65 ---- ---- 34 2 And the carry gets added to implied zeros: 11 1 056 34 + 078 + 65 ----- ---- 134 2 Same thing in base 7: we add 3 and 6, plus the carry, to get 10... or 13 in base 7... and we carry the same way: 11 11 056 034 + 078 + 065 ----- ----- 134 132 So the point of all this is, the algorithms are exactly the same! The only thing that changes is that when you count in base 7, you run out of digits more quickly, so you have to regroup more often. Try this with some other operations, and see if you can make sense of those, too. Let me know if you need more help. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 08/04/2007 at 05:24:14 From: Anne Subject: Thank you (Could you please explain base 7 to me?) Thank you very much for helping me this site is really very helpful. Anne |
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