Design 2 bit Synchronous up counter using T Flip flop?

These are the following step to design a 2 bit Synchronous up counter using T Flip flop

Step 1: To design a synchronous up counter, first we need to know what number of flip flops are required. we can find out by considering a number of bits mentioned in the question. So, in this, we required to make 2 bit counter so the number of flip flops required is 2 [2ⁿ where n is a number of bits].

Step 2: After that, we need to construct a state table with an excitation table.

Note: To construct an excitation table from the state table you should know the excitation table of the respective flip flop, in this case, it is T flip flop. So check the excitation table forT flip flop Which is:

T Flip Flop Excitation Table

So, the above table is the excitation table for T Flip Flop.

State Table with  excitation  table

Above the table is created as per follow :

When Q₂ =0 which is the present state and Q₂‘=0 which is the next state then T₂ becomes 0 [As per excitation table, have a look ]
Similarly, if Q₂ is 0 and Q₂‘ is 1 then T_{2 becomes} 1.
In a similar way, it goes on.

Step 3: After making the excitation table the next thing to do is dig out the equation from the boolean algebra or K map for the design of the counter. So For T₁ and T₂ we got 1 and Q₁ .

K-Map

For T_{2  Flip flop,}

For T₁ Flip flop,

Step 4: Lastly according to the equation got from K map create the design for 2 bit synchronous up counter.