This website is really nice for understanding what happens in an resistance ladder:

https://www.laiv.audio/post/what-is-an-r2r-dac-a-beginners-guide-to-resistor-ladder-digital-to-analog?srsltid=AU7gw4W5OnnDf9f2VvbnIL5Hj4_s42lz_eSTgxssjb_VcFGFYMkOUEpo

Lets look a little deeper. I build the circuit in a simulator (https://www.circuitlab.com/)

There are four voltages on the bottom. You can adjust all of them. But remember we are building a digital circuit and they can only be ones and zeros (or 3.3 V and 0 V).

The upper right voltmeter is the output voltage.

So let’s play with the numbers

[input voltages] -> out put voltage

• [0,0,0,0] -> 0
• [1,0,0,0] -> -0.125
• [0,1,0,0] -> -0.250
• [1,1,0,0] -> -0.375
• [1,1,1,1] -> -1.875

Think about how a base two number works (*We can adjust with resistors values

base 10	base 2	output*
0	0 or 0000	0
1	1 or 0001	-0.125
2	10 or 0010	-0.250
3	11 or 0011	-0.375
4	100 or 0100	-0.500
5	101 or 0101
6	110 or 0110
7	111 or 0111
8	1000
9	1001