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If the output of the state machine, or any of the logic that the state machine operates on, is asynchronous, gray codes are typically preferred. This is due to the fact that asynchronous circuits are not protected from race conditions and glitches. Thus, the path differential between two bits in the state register can cause unexpected behavior and will be very dependent on layout and parasitics. Consider the output encoding for a Moore machine as shown in Figure 14.14. In this case, state transition events will occur where a single bit will be cleared and a single bit will be set, thereby creating the potential for race conditions. The waveforms illustrating this condition are shown in Figure 14.15. One solution to this problem is to use gray encoding. A gray code only experiences a single bit change for any transition. The fact that gray codes can be used to safely drive asynchronous outputs is apparent after analyzing the structure of coding scheme. To construct a gray code, use the mirror-append sequence as described below. 1. Begin with a 0 and a 1 listed vertically. 2. Mirror the code from the bottom digit. 3. Append 0 to the upper half of the code (the section that was copied in the mirror operation). 4. Append 1 to the lower half of the code (the section that was created in the mirror operation).
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Example moore machine output.
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14 Synthesis Optimization
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This sequence is illustrated in Figure 14.16. As can be seen in Figure 14.16, a gray code will only experience a single bit toggle for every state transition and thus eliminates race conditions within the asynchronous logic.
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Use gray codes when driving asynchronous outputs.
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Aside from conditions such as described above, one-hot encoding is typically preferred for FPGA design. This is because FPGAs are register rich, there is no decoding logic required, and because it is usually faster. For these reasons, most state machines will be replaced with a one-hot structure, so for good design practice and to reduce overall run time it is advised to design all state machines with one-hot encoding unless there is a compelling reason to do otherwise.
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14.4 FSM Compilation
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14.4.1 Removal of Unreachable States
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Most state-machine compilers will remove unused states and may be intelligent enough to detect and remove unreachable states. For most applications, this will help to optimize both speed and reduce area. The main application that would require the retention of unreachable states would be for high-reliability circuits used in aviation, by the military, or in spacecraft. With ultrasmall geometries, particles of radiation from solar or nuclear events can cause ip- ops to spontaneously change states. If this happens in a circuit that is critical to human life, it is important to ensure that any combination of register states has a quick recovery path. If every possible state in a FSM is not accounted for, it is possible that such events could put the circuit into a state from which it cannot recover. Thus, synthesis tools often have a safe mode to cover all states even if they are unreachable through normal operation. The following module contains a simple FSM that continuously sequences through three states after reset. The output of the module is simply the state itself.
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module safesm output [1:0] input reg [1:0] ( oCtrl, iClk, iReset); state;
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// used to alias state to oCtrl assign oCtrl = state; parameter STATE0 STATE1 STATE2 STATE3 = = = = 0, 1, 2, 3; STATE0;
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always @(posedge iClk) if(!iReset) state <= else case(state) STATE0: state <= STATE1: state <= STATE2: state <= endcase endmodule
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STATE1; STATE2; STATE0;
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The implementation is simply a shift register as shown in Figure 14.17. Note that if bits 1 and 2 are errantly set simultaneously, this error will continue to recirculate and generate an incorrect output until the next reset. If safe mode is enabled, however, this event will cause an immediate reset as shown in Figure 14.18. With the implementation of Figure 14.18, an incorrect state will be detected by the additional logic and force the state registers to the reset value.
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