Also, this could be called a 10 line to BCD (Binary Coded Decimal) encoder. It works just like a phone number pad.
A 10:4 encoder works just like a 16:4 encoder, except that it uses 6 fewer lines, so only numbers 0000 - 1001 (0 - 9) are acceptable outputs.
NOTHING. 0000. 0
BUTTON 0. 0000. 1
BUTTON 1. 0001. 1
BUTTON 2. 0010. 1
BUTTON 3. 0011. 1
BUTTON 4. 0100. 1
BUTTON 5. 0101. 1
BUTTON 6. 0110. 1
BUTTON 7. 0111. 1
BUTTON 8. 1000. 1
BUTTON 9. 1001. 1
Each of the 10 lines is encoded to a digital number, and a 4-bit BCD number has 10 combinations. This is why it's called a decade (10) encoder, or BCD encoder.
The opamp provides the "Got Something" signal to distinguish between "Nothing" and "0".
I made it from the ADC technique like before (https://everycircuit.com/circuit/4533694924324864 ), but this is not a very good practical solution. In real life, use an encoder chip (like 74C922 or 74LS148). But EveryCircuit doesn't have one, so...
Have fun with electronics!
