the picture says it all
Just plug it into appropriate setting.
You want alpha of image 2 as a factor of the addition of color. Plug it into factor of MixRGB node.
You want alpha of Image 2 as a transparency value. Plug it into factor of a mix shader.
You want alpha of image 2 mixed with alpha of Image 1. Add a math node to combine them.
In fact, your picture says absolutely nothing about what you want.
But I am pretty sure that there is already an existing solution to most common cases that have been encountered since 5 years of existence of Cycles.
the factor of mix shader shouldn’t be the input of the alpha channel. it only serves to mix 2 shaders. the factor determains the infeluence of these shaders
If you mix a shader with a transparent shader, it is legitimate to use alpha as a factor.
Alpha channel is not different than a mask. As is, it can be connected to any factor and be subject of any mathematical operation.
You can plug it into a strength value or color it.
Cycles nodes offers you a large freedom.
Don’t stay stuck to your habits acquired from other softwares having rigid workflows.
i want to make myself clear here. the solutions you provided are not wrong. they do work. but after working with many realtime applications and other shaders in the past i can say for certain the secondary albedo maps have nothing to do with transparency shader. the way you do it in cycles is a hack. you should be able to use your alpha maps with the standard shader or the mixRGB node.
I don´t understand what do you want to achieve…
what at do you want the second alpha to do?
Cheers.
That is the mixRGB node not the mix shader node in your screen grab so this is making every thing really confusing to follow along. What do you actually want to do, several people have asked this because its not really clear.
I think the issue here is the lack of definition of mazedev’s words ‘I want the alpha channel of Color2 to work’. I assume here ‘Color2’ actually means the second Image Texture. The question arises - HOW should the alpha channel work? Alpha channel is just another channel in a texture file. Anything can be stored there. In RGB channels red green and blue values are stored - that’s kind of a rule, but there are really no rules about what information should be in the alpha channel so it is logical to specify what exactly it should do. It is common to use it for transparency, but in 3d it can mean transparency of a texture or transparency of a shader or mix factor of anything and you also can use the alpha channel for storing ANY other information - like roughness for example or mask to define particle emission or for probably thousands of other things. It seems logical to me - it would make no sense to have functionality that would limit possible uses of alpha channels hard-coded in any shaders, would it?
can say for certain the secondary albedo maps have nothing to do with transparency shader. the way you do it in cycles is a hack. you should be able to use your alpha maps with the standard shader or the mixRGB node.
You can do that.
And you can do that.
So if A is R[SUB]A[/SUB], G[SUB]A, [/SUB]B[SUB]A[/SUB], A[SUB]A
[/SUB]and B is R[SUB]B[/SUB], G[SUB]B, [/SUB]B[SUB]B[/SUB], A[SUB]B
[/SUB]Does he want the result then to be
R = R[SUB]A[/SUB] + R[SUB]B,[/SUB] G[SUB]A[/SUB] + G[SUB]B[/SUB], B[SUB]A[/SUB] + B[SUB]B[/SUB], A[SUB]B[/SUB] OR A[SUB]A[/SUB]
Several solutions posted, and dismissed, without clarifying the objective. Perhaps an image of the wanted end result would help?
is mainly same story again 
what blender needs is an open mind
what everyone needs, shows…
so enjoy;)
explanations are sufficient, consider the case closed.
here is what i meant. there is an option to directly tap into the alpha channel
That is something similar to a “set Alpha” node, I’m not sure how is it called in Blender, but with that you just can define the alpha channel of an RGB texture, but in any case, that has no sense unless you have 1 picture with the RGB data and 1 picture with the Alpha data, and you want to define the second picture as the Alpha of the first picture, but I’m not sure if that was what you meant.
Cheers.