Provided are a semiconductor device and a rechargeable power supply unit which are capable of accurately detecting an overcharge state of a battery even in a case where the battery is charged with a sine wave charger. In a case where a ½ cycle of a charging voltage of the sine wave charger is shorter than a delay time for cancellation of an overdischarge state, when it is detected that a voltage of the battery in the overdischarge state exceeds an overdischarge detection voltage and becomes equal to or higher than an overcharge detection voltage, a delay circuit sets the delay time for cancellation of the overdischarge state to 0 seconds.