This work developed DNA amplifier logic gates (AND-OR, OR-AND, FAN-IN, FAN-OUT, and 4-bit square-root circuits) using a flap endonuclease 1 (FEN1)-catalyzed signal amplification reaction, for the fastest and compact DNA computing. Moreover, the logic circuit can use input strands with concentrations of less than 1 nM, which is more than 100 times lower than the input concentration of other DNA logic circuits, providing a promising methodology for constructing fast and compact DNA computations.