Calculation of time needed to crack DES with my CPU I have a laptop that has the CPU and the RAMs shown below in the images. 

My question is that, using this CPU and the RAMs, how much time would it take for me to crack an old school DES algorithm with 56 bit key.

I have read on the web that it was cracked in 56 hours using a 220,000$ machine in 1998. But I believe we are much more advanced in computing speed after 15 years and counting.

I would also highly appreciate if someone can explain the steps of how such a calculation takes place.!
I can't provide you with good numbers without actually benchmarking on your system.

All I can provide you with are estimates, based on the fact that Serpent is roughly as fast as DES. Of course the figures I can give you aren't actually brute-force figures but rather how much data can be encrypted per time, but this should give a solid estimate of the required time.

The general approach is to measure how many keys per second you can try and then divide $2^{56}$ by this number which will result in the number of seconds you'll need.

So let's estimate for Serpent with 56 bits. Serpent can get up to 0.16 GB/s on your machine as this is mainly computation bound. 0.16 GB is roughly $2^{24}$ blocks for DES, meaning you can roughly try $2^{24}$ keys per second. This means you need $2^{56}/2^{24}=2^{32}$ seconds for this which is equal to 136 years.

I'm sorry but I doubt this is feasible for you.
Note that even the brand-new Intel Core i7 6700K can only do 0.47 GB / s meaning an i7 6700K would also still require roughly 45 years. And to get even more crazy: the Intel Core i7 5960X is the best consumer CPU as of now can only do 0.63 GB / s resulting in 34 years. Now finally consider the currently strongest possible server mainboard running 8x Intel Xeon E7-8890v3 with 18 cores. There's no measured benchmark out there but I assume the performance to scale linearly with the number of cores (75 MB/s per core) and the frequency (62.5 MB/s with E7's freq). This would mean that this board could do 9GB / s of Serpent meaning $2^{30}$ blocks and thereby $2^{26}$ seconds being equivalent to 2.12 years (however this board would roughly cost $56k in 2015).