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— taswelll

- joined
- ago

## recent posts

have some powers of two, as a treat: 4294967296 2147483648 1073741824 536870912 268435456 134217728 67108864 33554432 16777216 8388608 4194304 2097152 1048576 524288 262144 131072 65536 32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1

yes! ax^{5} + bx^{4} + cx^{3} + dx^{2} + ex + f = f + x(e + x(d + x(c + x(b + ax))))

this is right! this is how binary to decimal conversion works. the BNs are the the powers of two: each digit is the previous increased by itself => each digit is the previous multiplied by 2 => nth digit is 2 to the nth power.

positional base for a given B works the same way if you change "add all the powers of two where there is a one" to "add all the powers of K multiplied by the corresponding digit" (these are equivalent if K is 2; multiplying something by 0 is 0)

say you want to get the decimal number of the octal number 5756. let's get the powers that we need:

- 8
^{3}= 512 - 8
^{2}= 64 - 8
^{1}= 8 - 8
^{0}= 1

and 5*512 + 7*64 + 5*8 + 6*1 = 3054. this will work for every octal(/binary) number!