DNA computing circuits are favored by researchers because of their high density, high parallelism, and biocompatibility. However, compared with electronic circuits, current DNA circuits have significant errors in understanding the OFF state and logic "0". Nowadays, DNA circuits only have two input states: logic "0" and logic "1", where logic "0" also means the OFF state. Corresponding to an electronic circuit, it is more like an on-off switch than a logic circuit. To correct this conceptual confusion, we propose a three-level circuit. The circuit divides the input signal into three cases: "none", logic "0" and logic "1". In subsequent experiments, 34 input combinations of the primary AND gate, OR gate as well as secondary AND-OR and OR-AND cascade circuits were successfully implemented to perform the operation, which distinguished the OFF state and logic "0" correctly. Based on this, we successfully implemented a more complex voting operation with only 12 strands. We believe that our redefinition of the OFF state and logic "0" will promote tremendous developments in DNA computing circuits.