The CD4013 or IC-4013 is a CMOS logic chip with two D-Type (DATA) Flip-flops. A clock pulse flow to C (clock pin), will store the data at the D input. Connect clock and a both Q output to make a toggle flip-flop for counting.
Can we use AND and OR logic gate with Diodes? Yes, we can. The past, we have used only a digital logic circuit by IC. But, in truth. We do not need any ICs. Use Switches or Diodes or transistors connected as a logic circuit.