I just can’t stop laughing at it!

The Bass Model is used as a quantitative tool for forecasting the diffusion of new technology products.
Innovators: Customers who learn about new products from sources other than previous adopters, such as from advertising
Imitators: Customers who learn about new products from previous adopters
A simple formula of calculating the diffusion is as follows:
Let (M) be the size of the market
Let (P) be the rate of adoption by innovators
Let (Q) be the rate of adoption by imitators
Let (Nt-1) be the cumulative number of adopters in the previous time period
Let S(t) be the number of new adopters during time period t
Then, we have the following,
Thus, the diffusion rate is forecasted to be at 1.25
Example:
Innovators (P) : 0.1 (10%)
Imitators (Q) : 0.3 (30%)
Market (M) : 10 millions
Nt-1 : 5 millions already adopted the product
S(2) = (10-5) * (0.1 + 0.3 [5/10]) = (5) * (0.1 + 0.15) = 1.25
Thus, the diffusion rate is forecasted to be at 1.25 for the 2nd year.
* You will need to have an existing Paypal business account to retrieve the API credentials.
You can access the Paypal API credentials through this link: https://www.paypal.com/us/cgi-bin/webscr?cmd=_get-api-signature&generic-flow=true

Alternatively, you may wish to follow the following step by logging into Paypal:
1. Log in to your PayPal Premier or Business account.
2. Click the Profile subtab located in the top navigation area.
3. Click the API Access link under the Account Information header.
4. Click the Get Started link under the Request API Credentials heading.
5. Click the My selling preferences sub option in left sidebar.
6. Click the Update option for API accessitem
7. Complete the API Credential Request form by clicking the agreement checkbox and clicking Submit.
8. You will now get the API username, password and signature.
The above steps are taken from http://www.putler.com/support/faq/how-to-get-paypal-api-username-password-and-signature-information/
Referencing the API error codes is useful when debugging Paypal payment gateway.
Please refer to https://www.x.com/developers/paypal/documentation-tools/api/errorcodes for a list of Paypal error codes.
Navigate to VERSION.txt under the directory /lib/Cake
The version number is appended at the end of file.
A cheat sheet post for Facebook image size in order to fit exactly:
Cover Photo
Dimension: 851 pixels x 315 pixels
Shared Photo on Timeline
Dimension: 403 pixels x 403 pixels
Highlight / Milestone
Dimension: 843 pixels x 403 pixels
Reference :: http://www.jonloomer.com/2012/03/07/dimensions-for-facebook-timeline-for-pages-infographic/
For convenience sake, here is the recommend size for Facebook cover photo:
In addition, the image file should be kept as sRGB JPG file with a filesize of less than 100Kb for best quality and fastest loading time for the page.
Facebook also implements guidelines that the cover photo must adhere to:
Resource: https://www.facebook.com/help?faq=+276329115767498
The video below explains the concept of simplification when using K-Map to find the minimal Sum-of-Expressions (SOP):
First of all, you need to understand the truth table for Exclusive-OR gate:
| Input | Output | |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
With this in mind, we move on to converting binary code to gray code.
Suppose we want to convert decimal 10, binary value of 1010 to gray code, the first step is to retain the most significant bit(MSB) of the binary. Hence,
1 0 1 0 (binary)
1 x x x (gray)
where x is still unknown.
Then, we take the adjacent pair of binary code to derive the 2nd significant bit of the gray code. Based on the truth table, 1 and 0 give us a 1 :
1 0 1 0 (binary)
1 1 x x (gray)
Then we move on to the next adjacent pair of binary code to get the 3rd significant bit of the gray code, with reference from the OR truth table :
1 0 1 0 (binary)
1 1 1 x (gray)
and lastly,
1 0 1 0 (binary)
1 1 1 1 (gray)
Therefore, the gray code of 1010 (decimal 10) is 1111.
Now, to convert gray code to binary code, we employ the same technique with the exception that we take the previous significant bit of the gray code and the next binary code to get the output.
Suppose we want to convert decimal 6, gray code value of 0101 to binary code, the first step is still to retain the MSB of the binary. Hence,
0 1 0 1 (gray)
0 x x x (binary)
where x is still unknown.
From here, we move on to take the previous significant bit of the gray code and the next binary code, which is 1 and 0. 1 and 0 give us 1.
0 1 0 1 (gray)
0 1 x x (binary)
and then we move on….
0 1 0 1 (gray)
0 1 1 x (binary)
0 1 0 1 (gray)
0 1 1 0 (binary)
Thus, the binary code of 0101 (decimal 6 in binary) is 0110.
To convert a decimal to 2-complement (2s), you first convert the decimal to binary and invert the bit. From there, you plus one and that would be the 2s of the decimal.
The 2-complement of 5, which is -5, is:
First step: Invert the bits of 5 in binary -> 1010
Second step: Plus one to the inverted bits -> 1011
Hence, the 2-complement of 5 would be 1011
Now, to convert a 2-complement back to a decimal….
The algorithm is as follows:
“If it is positive, simply convert it to decimal. If it is negative, make it positive by inverting the bits and adding one. Then, convert the result to decimal. The negative of this number is the value of the original binary.” quoted from Mississippi College.
First step: The sign bit of 1101 shows that it’s a negative decimal. Hence, we invert the bits -> 0010
Second step: We add one to the inverted bits -> 0011
0011 in decimal is 3. The negative of 3 is -3. Hence, the original binary value of 1101 is -3.