“How many Flip Flops would be required for a 12-state, state machine?” Possible answers:
a. 3
b. 4
c. 5
d. 14
e. 2
f. 12
g. 16
h. 13
i. 8
j. 11
The correct answer and explanation is:
To determine how many flip-flops are needed for a state machine with 12 states, you need to calculate how many binary bits are required to uniquely represent 12 states. This is because each flip-flop can store a single binary bit, which can represent two states (0 or 1).
The general formula to determine the number of flip-flops (or bits) required is based on the binary representation of the number of states. Specifically, you need to find the smallest number nn such that 2n≥number of states2^n \geq \text{number of states}.
For a 12-state machine, let’s check: 23=8(not enough for 12 states)2^3 = 8 \quad (\text{not enough for 12 states}) 24=16(this is enough to represent at least 12 states)2^4 = 16 \quad (\text{this is enough to represent at least 12 states})
Thus, 4 flip-flops are required because 24=162^4 = 16, which is the smallest power of 2 that can represent 12 states.
Answer: b. 4
In general, the number of flip-flops needed increases as the number of states increases. For example, if the number of states were 25, 25=322^5 = 32 flip-flops would be necessary because 32 is the smallest power of 2 that can cover 25 states.
Using flip-flops to store state information is crucial in digital design, especially for finite state machines (FSMs), which are widely used in hardware design, such as control units, counters, and memory systems. Each flip-flop essentially helps track the state of the system by storing a binary value, and the number of flip-flops determines the range of states that can be uniquely identified.