Bitwise AND operation backwards

[Mc_Topaz]

Homework Statement

At my company we calculate a product's serial number from a MAC address provided with the unit. One of the equations is done with a bitwise AND operation of two integers. I have tried to run that equation backwards but with no result.

Variables and data:

V = The source value to do the bitwise AND operation with
C = A known constant to use in the bitwise AND operation
S = Result of bitwise AND operation

Let say: V = 10, C = 6

Homework Equations

The equation forward is: V & C = S => 10 & 6 = 2

In binary:

1010 = 10
0110 = 6
-----
0010 = 2


Now I just want to reverse that process and calculate 10 from 6 and 2 in some way.

Don't try with: C + 2S (6 + (2*2)) works just in this case.

The Attempt at a Solution

I tried the opposite way by changing V for S:

2 & 6 = 2

In binary:

0010 = 2
0110 = 6
-----
0010 = 2


The problem occurs when one of the bits in the V is 1 and the equivalent bit in C is 0. The bit in S will then be 0 and V's bit can never return to 1.

Any suggestions?

/Mc_Topaz

 

[uart]

Unfortunately that's just not possible as it's a many to one mapping. Of the three main two input binary operators (AND OR XOR) only XOR is invertible like that.

 

[Strants]

It would be possible if you also knew V & ~C, though. Since A & B only has ones where both A and B have ones, and ~B has ones only where B has zeros, V & ~C has the 'missing ones' from the other calculation.

 

[uart]

It would be possible if you also knew V & ~C, though. Since A & B only has ones where both A and B have ones, and ~B has ones only where B has zeros, V & ~C has the 'missing ones' from the other calculation.

Actually "V" is the thing he's trying to find (given S and C). Knowledge of ~C provides no new information and doesn't help with the original problem. Since he knows C then he already knows ~C anyway.

 

[DeeNos]

The bitwise AND operation is a logical operator that compares the corresponding bits in two numbers and returns a new number with a 1 in each bit position where both numbers have a 1. This operation is not reversible, meaning that you cannot determine the original numbers from the result of a bitwise AND operation. This is because the operation discards information about the individual bits and only considers the overall pattern of 1s and 0s.

In your example, the result of the bitwise AND operation (2) does not contain enough information to determine the original numbers (10 and 6). Therefore, it is not possible to calculate 10 from 6 and 2 using a bitwise AND operation.

If you need to calculate the original numbers from the result of a bitwise AND operation, you will need to use additional information or equations. For example, if you know the value of C and the result of the operation, you can use algebra to solve for V. However, this will require more information than just the result of the bitwise AND operation.