The quickest way to create Photoshop binary code patterns is to set up some guides : View menu and then New guide layout and Set columns to 10 and Set rows to 10 (or 4 x 4 etc but if you make it too small the repetition is way more obvious). The settings for the guides do not need to be 10 and 10 (they could easily be 15 x 20 or 50 x 45 etc) but to create some level of randomness for the grid, you really do need at least a 10 x 10 setup and the guides are useful for the alignment of the characters, 0 and 1 but you can also select the entire row or column and use the alignment tools to align them as well. The guides are just to give some idea of a more uniform positioning. OK, once you have the guides then the next thing to do is to fill it with 0 and 1 in the cells
The next step is to go to one of the 'cells' and add a 0 in a font, perhaps Verdana or courier new or whatever you want. You can always change them later. Go to the type tool and set color and set font(you can use any of the fonts available to you) and set size and that depends on the size of the document and the grid, what works well in one will not be great for another. I would suggest have about 80% of the size of the cell so if the cell is 100pt then perhaps 80pt for the numbers. Click the art board in the middle of one of the cells and add 0 and then duplicate that character and move to another cell and change the 0 to 1.
Now go to the layer menu and smart objects and convert. Do the same for the 0 as well, both are now smart objects and Select the 0 or 1 and hold down the option / alt to duplicate the 0 or 1 and Shift that randomly to another cell. You don't have to convert to smart objects, if you want to make random changes to all your 0 and 1 characters such as have them all with unique fonts then don't change them to smart objects. If you want consistency then changing them to smart objects is perhaps more useful.
Repeat that for the 0 or 1 over and over until you have filled all the cells with the 0 and 1 numbers. Now select an entire row or column and then use the align tools found in the control bar. Repeat this for all the rows and columns so now you should have a complete set up of 0 and 1 cells.
If you do not flatten the work, you can always shift the combination of 0 and 1 cells around and so if you want to, save the 0 and 1 layers as a PSD file to use as an endless source of different combinations of 0 and 1 (or perhaps use X and Y or any other letter combinations as well). You can always save the work to the creative cloud library (window and libraries) for future use
Edit menu and define pattern - it is now stored as a preset
Layer menu and new fill layer content aetc and select the newly designed preset and create a new layer, set the scale, set the rotation, apply effects etc to it, perhaps create multiple layers, use with the masks, add in adjustments and more
Why did I suggest creating them as smart objects? You can change a single cell and the change will be reflected throughout the entire design. Say you decide to change the '0' smart object cell and change it to a different font or perhaps a different color, you can in seconds. Of course, you don't need to use smart objects and you can just create all the cells / numbers 0 and 1 as separate cells and then edit them individually (up to you)
Go to the layers panel and double click the layer thumbnail / smart object and you will then find yourself in a PSB file and edit the number (0 or 1) and change the size or color etc and perhaps the 1 to a 0 etc - note at all times, the type is still live and can be edited to anything such as A or B instead. Close the PSB (saving any changes)
You will now see the change in all the other related smart object designs so if you have changed the color from black to red then they will become red (the other smart objects will be unchanged). You will still have to use the edit menu define command to add the design to the presets, any changes will not be reflected in the panel until you have done this. You can also save it to the brushes panel as well and use that alongside the tiles.
You can also use effects with the artwork such as adding blurs or adding other colors to the background or perhaps using brush tools such as blurs or smudge to alter individual characters. The art can be modified in countless ways such as by using camera raw filter or twirl distortion filter effect etc You can apply it to the source designs such as twirl or distorting it or using displacements etc
You can also re-color the design using adjustment layers as they are non destructive effects, the adjustment layers can be added above and the colors of the tiles can be changed in endless ways