Your first statement is correct; your second statement is incorrect, considering that large portions of electronic hardware are computer electronic hardware, and almost all modern computer electronic hardware doesn’t work without software^(1).
It is possible to hardcode functions into a chip; that probably doesn’t count as software.
Your first statement is correct; your second statement is incorrect, considering that large portions of electronic hardware are computer electronic hardware, and almost all modern computer electronic hardware doesn’t work without software^(1).