Question

Design a modulo-11 up/down counter using a regular modulo-16 counter and any combinational logic. The modulo-11 up/down counter has four modes; count up by 1, count up by 2, count down by 1, and no count. A formal description of the modulo-11 up/down counter is shown below.

Inputs: ctrL0, ctrl-1 є {0, 1} State/Output:s (0,1, 10) The state transition function is defined as:
{ s(t) if ctrl_0=0 and ctrl_1=0
s(t+1)= { (s(t)+1mod11 if ctrl_0=0 and ctrl_1=1
{ (s(t)+2mod11 if ctrl_0=1 and ctrl_1=0
{ (s(t)-1mod11 if ctrl_0=0 and ctrl_1=1
You can assume that-1 mod 11 = 10.

Answer 1

To design a modulo-11 up/down counter, you can use a regular modulo-16 counter and combinational logic to modify the state transition function.

Step-by-step explanation:

To design a modulo-11 up/down counter, we can use a regular modulo-16 counter and combinational logic. We can modify the state transition function of the modulo-16 counter to implement the desired functionality for the modulo-11 counter. For example:

1. If ctrl_0 = 0 and ctrl_1 = 0, the counter remains in the current state s(t).
2. If ctrl_0 = 0 and ctrl_1 = 1, the counter increments by 1 modulo 11: s(t+1) = (s(t) + 1) % 11.
3. If ctrl_0 = 1 and ctrl_1 = 0, the counter increments by 2 modulo 11: s(t+1) = (s(t) + 2) % 11.
4. If ctrl_0 = 1 and ctrl_1 = 1, the counter decrements by 1 modulo 11: s(t+1) = (s(t) - 1 + 11) % 11.