The conversion of a binary number of to decimal

[Mikl__]

10-2=8

multiply the number to 8 in the k-step, k-leading digits and subtract the result from (k+1)-leading digits. If the binary number contains k digit, then the process will be completed by k-1 steps
10001101₂ -> 141₁₀

Code Select Expand


1.0001101
- 8                  (1*8=8)
-------------
   2.001101
- 16               (2*8=16)
   ------------
    4.01101
  - 32              (4*8=32)
      ----------
       8.1101
     - 64           (8*8=64)
       ---------
       17.101
      -136         (17*8=136)
       ---------
        35.01
      - 280        (35*8=280)
          -------
           70.1
         - 560    (70*8=560)
            ------
            141

[dedndave]

that makes no sense to me   :lol:

where do the decimal points come from ?
maybe provide some explanation for each step

[Mikl__]

Hi, dedndave!
it is not a decimal point, it is to separate the next digit to multiply, at each step, we move the point to next digit

conversion of a decimal number of to  binary

remember power of 2 (2¹⁰=1024, 2⁹=512, ... 2³=8). For example, convert decimal number 147 to binary, 2⁷=128<147<2⁸=512

	1	2	3	4	5	6	7	8
147/128=1 remainder 19	1
19/64=0 remainder 19	1	0
19/32=0 remainder 19	1	0	0
19/16=1 remainder 3	1	0	0	1
3/8=0 remainder 3	1	0	0	1	0
3/4=0 remainder 3	1	0	0	1	0	0
3/2=1 remainder 1	1	0	0	1	0	0	1
1/1=1	1	0	0	1	0	0	1	1
14710=	1	0	0	1	0	0	1	12

[dedndave]

division is slow - work it in the opposite direction
but, you are just assigning a value for each bit - nothing new, there

[Mikl__]

dedndave,
of course, nothing new, because there is a built-in Windows calculator

[dedndave]

if you want to work on base conversion between any bases, google for "horner's rule base conversion"

[Mikl__]

google for "horner's rule base conversion"

dedndave,
thank you, but I know it