What is the base 10 value of this number? d2d1d0 321 Oh, I forgot to tell you that digit 2 is base 2, digit 1 is base 3 and digit 0 is base 4. (This is a number. The digits are coupled with carry and all that.) There is no prize for this.
d0d1d2 ? then 321 = 3*4^2 + 2*3^1 + 1 = 55 (in base 10) edit : mixed bases..??!! - still i couldn't find out the meaning of the above..! never mind. no prize..
Yep, I had them backward. Digit 2 is base 4, digit 1 is base 3 and digit 0 is base 2. The way I had them the number would have been 123 which has the same answer. Dyslexia strikes again. Everneo, You are almost right. The answer is: V10 = d2*b1*b0 + d1*b0 + d0 V10 = 3*(3*2) + 2*2 + 1 = 23 The next number after 321 is 000 The digit base of this number is b2*b1*b0 = 24 It the number had been all base 4 then V4 = 3*4^2 + 2*4 + 1 = 57 Note that base powers are a special case when all bases are the same. There are many numbers in between equal base numbers. I came on this with real numbers as two digits. I realized they did not have to have the same base, so there are other numbers with mixed bases. What good this is I do not know. I am now trying to find out how many there are.
How could we have known that was how to solve it? That's not how normal base numbers work at all. But you know that..... since you calculated it correctly if the base was 4??? Why would you need to multiply the first digit by two different bases? Did you just make this method up? d2*b1*b0??? Where does that come from? Have I missed a whole area of dealing with bases? Can someone help me figure out where this all came from? Please Register or Log in to view the hidden image! Adam
Adam, Yes, I just made this up. Base is a counting number from 0 to N. A single digit can be any number in that. The number of wires that make the number make a digit. I use base = 256 for my robots. To convert any base b to decimal multiply the digits with the digit base. For 3000 years we have been using same base for all digits ,which make powers when multiplied. 123 is a number. In base 10 it is: V = 1*100 + 2*10 + 3 = 123 which means it took 123 counts from 0 to get to it. With multi digits, using powers, there are great gaps in the base number. For two digits we have 4 9 16 25 36 which leave lots of gap. It gets worse with more digits. I said, what if all digits had their own base? A good place to start is have ascending numbers for each digit base. That gives us factorials instead of powers. Take 123 again. Digits are d2, d1, d0. Let base be 2 3 4 Then V = 1*3*4 + 2*4 + 3 = 23 We just had to take 23 counts to get here. Don't know how to do this in hardware. Might be useful because you can make a number more sensitive at one end. Still working. As you can see, I don't have much to do.
We're good to there Please Register or Log in to view the hidden image! I have a degree in math so all that was well known to me. Still good. bolding by me Why? This is what I don't understand. Why do you start multiplying bases? I would think the natural way to go would be like everneo did. 321 with bases 4,3,2 would look like: 3*4^2 + 2*3^1 +1*2^0 = 55 This stuff about factorials.... it seems an entirely new convention that you have made up (not a bad thing in my mind Please Register or Log in to view the hidden image!). What I was wondering was what line of reasoning lead you to treat the 'multiple base' number like that. I don't see it. Just in case it's just me, does anyone else see the line of reasoning being used here? hlreed, do you understand what I mean? I think if you are going to mix bases, you would proceed as everneo did, as I explained above. That is just my opinion, I was wondering what reasoning lead you to use this new techniuque. And btw, no attacks here, I'm just wondering. Who knows, if you've invented a new kind of convention for numbers, it may very well become useful in who knows what fields someday! Please Register or Log in to view the hidden image! Adam
I have no idea what this is good for. Here are the codes for 321 when b2 = 4, b1 = 3 and b0 = 2 2 1 0 value 0 0 0 0 0 0 1 1 0 1 0 2 0 1 1 3 0 2 0 4 0 2 1 5 1 0 0 6 1 0 1 7 1 1 0 8 1 1 1 9 1 2 0 10 1 2 1 11 2 0 0 12 2 0 1 13 2 1 0 14 2 1 1 15 2 2 0 16 2 2 1 17 3 0 0 18 3 0 1 19 3 1 0 20 3 1 1 21 3 2 0 22 3 2 1 23 0 0 0 So, there you are with codes and count.
<i>I use base = 256 for my robots</i> That must be a real hassle. What unique symbol do you use to represent the digit with decimal equivalent 157, for example?
James, It is no hassle. 8 binary wires make a 256 base digit. All that means is it will go to 0 after 255 so i(1) will produce a saw tooth wave of amplitude 255. (i(1) is integral of 1 = 0 1 2 3 ... = N) I use 157 for the symbol of 157. Its bit configuration is 10011101 which you can also treat as a single symbol but it takes more space. I say these are the same thing. What matters is the content of the wires, not what you call it. A number is abstract. Here is the picture I use to show this. A digit is a wheel with symbols written around it. It has a click mechanism to click from one symbol on the wheel to the next. The number is the click count. Any symbols can be written on the wheel. They all reference the click count. You cannot write down a number. You can only write symbols. That is why I want explicit multiply symbols allowing long varable names. (This is already beginning to happen I notice.)
