S-DES is a toy cipher intended for learning, defined by Edward F. Schaefer, _A Simplified Data Encryption Standard Algorithm_, in [Cryptologia Volume 20, Issue 1, 1996 (paywalled with free preview)][1]. It has the same structure as [DES][2], and uses the same notations:

- bits vectors (such as key and data) are numbered starting from 1 "on the left"
- functions of bit vectors giving bits vectors are expressed by a series of decimal numbers, giving, for each bit of the output, the index of the corresponding bit in the input.

`P10` (which mimics PC1 in DES) transforms a 10-bit vector into a 10-bit vector, such that the j<sup>th</sup> bit of the output is at the index in the input given by the j<sup>th</sup> number in `3, 5, 2, 7, 4, 10, 1, 9, 8, 6`.<br>
For example, the 2<sup>nd</sup> bit in the output is the 5<sup>th</sup> bit in the input, because the 2<sup>nd</sup> number in the above sequence of numbers is 5.

`P8` (which mimics PC2 in DES) transforms a 10-bit vector into an 8-bit vector, such that the j<sup>th</sup> bit of the output is at the index in the input given by the j<sup>th</sup> number in `6, 3, 7, 4, 8, 5, 10, 9`.<br>
For example, the 7<sup>th</sup> bit in the output is the 10<sup>th</sup> bit in the input, because the 7<sup>th</sup> number in the above sequence of numbers is 10.

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The rest of the text in the question has the following meaning/rationale:

The key `K = 1010000010` of S-DES is a 10-bit vector. `K` is transformed using `P10`, yielding a 10-bit vector `CD0 = 1000001100`, which is split into two 5-bit vectors `C0 = 10000` and `D0 = 01100`.

In the first round,

- `C0` and `D0` each are [rotated on the left][3] by one, yielding `C1 = 00001` and `D1 = 11000`.
- `C1`and `D1` are joined into `CD1 = 1100011000`.
- `CD1 ` is transformed using `P8`, yielding `K1 = 10100100`.

In the first round,

- `C1` and `D1` each are rotated on the left by two, yielding `C2 = 00100` and `D2 = 00011`.
- `C2`and `D2` are joined into `CD2 = 0010000011`.
- `CD2 ` is transformed using `P8`, yielding `K2 = 01000011`.


  [1]: http://www.tandfonline.com/doi/abs/10.1080/0161-119691884799
  [2]: http://csrc.nist.gov/publications/fips/fips46-3/fips46-3.pdf#page=13
  [3]: http://crypto.stackexchange.com/questions/25238/how-does-rotl-work/25239#25239
  [4]: http://crypto.stackexchange.com/questions/25238/how-does-rotl-work/25239#25239