412.0.10 ok so going with dot product with 07312400508

In summary, the conversation discusses using the UPC scheme to determine the check digit for a given number. The process involves using a dot product with the number and a specific set of numbers, followed by taking the modulus of the result. The conversation also mentions the need to add a 12th digit in order to make the checksum zero mod 10.
  • #1
karush
Gold Member
MHB
3,269
5
Use the UPC scheme to determine the check digit for the number $07312400508$.

here is the example from the book
View attachment 8330
ok so going with dot product with 07312400508
\begin{align*}\displaystyle
&\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\
&= 0\cdot3+7\cdot1
+3\cdot3+1\cdot1
+2\cdot3+4\cdot1
+0\cdot3+0\cdot1
+5\cdot3+0\cdot1
+8\cdot3 \\
&=7+9+1+6+4+15+24\\
&=66\\
66mod10&=6
\end{align*}

so far?? but the number only has 11 digits
 
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  • #2
karush said:
ok so going with dot product with 07312400508
\begin{align*}\displaystyle
&\quad (0731 2 4 0 0 5 0 8)\cdot(3,1,3,1,3,1,3,1,3)\\
&= 0\cdot3+7\cdot1
+3\cdot3+1\cdot1
+2\cdot3+4\cdot1
+0\cdot3+0\cdot1
+5\cdot3+0\cdot1
+8\cdot3 \\
&=7+9+1+6+4+15+24\\
&=66\\
66\pmod{10}&=6
\end{align*}

so far?? but the number only has 11 digits
That is correct so far. You now have to add a twelfth digit so as to make the checksum zero$\pmod{10}$.
 
  • #3
Opalg said:
That is correct so far. You now have to add a twelfth digit so as to make the checksum zero$\pmod{10}$.
What would be the 12th digit?
 
  • #4
karush said:
What would be the 12th digit?
What do you have to add to 66 to get a multiple of 10?
 

1. What is the purpose of using dot product in this scenario?

The dot product is a mathematical operation that is used to determine the relationship between two vectors in a given space. In this scenario, it is being used to calculate the magnitude of the vector 07312400508 in the direction of the vector 412.0.10.

2. How is the dot product calculated?

The dot product is calculated by multiplying the corresponding components of two vectors and then adding those products together. In this scenario, the dot product would be calculated as (4*0) + (1*7) + (2*3) + (0*1) + (1*2) + (0*4) + (5*0) + (0*5) + (8*8) = 69.

3. What does the resulting value of 69 represent?

The resulting value of 69 represents the magnitude of the vector 07312400508 in the direction of the vector 412.0.10. This value can be used to determine the angle between the two vectors and their relative orientations.

4. Is the dot product commutative?

No, the dot product is not commutative. This means that the order in which the vectors are multiplied does affect the resulting value. In this scenario, if we were to calculate the dot product of 07312400508 and 412.0.10, the resulting value would be different.

5. How is the dot product useful in scientific research?

The dot product is useful in many scientific fields, such as physics, engineering, and computer graphics. It can be used to calculate work, energy, and momentum in physical systems, as well as determine the orientation of objects in space. In computer graphics, it is used to calculate lighting and shading effects in 3D environments.

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