To create an Affinity Photo binary code pattern, go to the tools panel and select the artistic text tool and then set the font and the size etc that you require as well as the color. You can make all kinds of variants by using different fonts and perhaps different colors and sizes for the 0 and 1 objects.
You don't have to use 0 1, you could use A B or you could add layer styles to the 0 and 1 etc or you could apply transformations to the set of characters used. You could also use live layers associated with them such as adjustments and blurs, distortions etc. You could add background shapes behind the 0 and 1 such as have all the zeros with a star behind them and all the ones have a circle etc.
You can create this by eye but it maybe very useful to go to the view menu and show grid and then go to the grid manager and set the value of the grid to 200px say. The same approach for creating a grid can be used in Affinity Designer as well (and you can create all of this in the same app as well)
Once you have this, type your first '0' in the grid cell and then use the alt / opt key to duplicate the zero. Repeat this multiple times and place the zeros throughout the cells. Change the 0 to 1 and then repeat that through the cells.
Once you have filled all the cells, go to the rectangle tool and then add a rectangle behind the 0s and 1s (use the arrange to back command / right click to access the arrange commands) and fill the image with the rectangle or the size you want for your design.
Select all the characters and the rectangle and then go to the layer menu and use the merge visible command.
Go to the layer menu and create pattern layer from selection. You can now re-size the pattern, rotate, shear etc. You can also add blurs and distortions to the layer though if you do that you may prefer to set the mirror option in the top left to be on. You may like to add maximum or minimum etc to modify the text. Or perhaps add some noise to the design or use different background papers.