Electrical – how to design a multiplier digital circuit using 4bit adders with output in BCD

Serial/parallel-load shift registers and bit rotations are going to work most naturally with a D flip flop, since they just send data straight through; binary counters are going to work most naturally with a T flip flop, since each counter bit C_k = C_k,previous XOR carry_k, where carry is the carry bit from the previous stage.

If you look at JK flip-flops, however, they are the "universal" flip-flop that can act as a D- or T- flip-flop depending on the input signals.

To get a D from a T, or vice versa, you need an XOR gate. To get a T from a JK, you just tie the JK inputs together. To get a D from a JK, you need an inverter, as the J/K inputs need to be opposites.

In your application, you've got enough complexity, that I suspect the gate counts are going to be very close, and it's probably not worth worrying about -- unless you have to optimize, in which case you'll just have to try it for each case.

IMHO, the D flip-flop is conceptually the simplest to use, and it works naturally with most of your operations, so I'd start with that.

No, you can not translate a (nontrivial) circuit that has memory to a combinatorial (feedback-less) circuit.

The outputs of a combinatorial circuit are by definition a function of its inputs (and nothing else).

Take the simplest non-combinatorial circuit: the Set-Rest memory cell (two cross-couples NANDS or NORS). When the inputs have the 'remember' value the outputs are a function of the past. This is simply not possible with any combinatorial circuit.