Abstract: In one embodiment, a power system includes a first power source having a first voltage, a second power source having a second voltage, and a controller. The controller is coupled to the first power source and the second power source. The controller compares the first voltage with the second voltage, controls the first power source to charge the second power source via a first switch and a second switch in a charging mode when the first voltage is greater than said second voltage, and controls the second power source to power a load such as a light-emitting diode (LED) light source via the second switch and a third switch in a load-powering mode when the second voltage is greater than the first voltage.

Abstract: A method of transforming a serial scrambler to a parallel scrambler, a parallel scrambler and a double-edge-triggered register with XOR operation are provided. The method transforms a serial scrambler to a parallel scrambler according to a characteristic polynomial: P ? ( x ) = ? q = 0 N ? c q ? x q ? ? or ? ? b ? ( i ) = ? q = 1 N ? c q ? b ? ( i - q ) . The method first determines a transformation formula: b ? ( kN + i ) = ? q = 1 N ? c q ? b ? ( ( k - R ) ? N + i + R ? ( N - q ) ) according to the parameters of the characteristic polynomial. The parallel bits Bj=[bMj, bMj+1, . . . , bMj+M?2, bMj+M?1] are arranged in order. The transformation number R=2t (the initial number of t is 0) is set. The parallel bits are replaced by the transformation formula.

Abstract: A method of transforming a serial scrambler to a parallel scrambler, a parallel scrambler and a double-edge-triggered register with XOR operation are provided. The method transforms a serial scrambler to a parallel scrambler according to a characteristic polynomial: P ? ( x ) = ? q = 0 N ? c q ? x q ? ? ? or ? ? ? b ? ( i ) = ? q = 1 N ? c q ? b ? ( i - q ) . The method first determines a transformation formula: b ? ( kN + i ) = ? q = 1 N ? c q ? b ? ( ( k - R ) ? N + i + R ? ( N - q ) ) according to the parameters of the characteristic polynomial. The parallel bits Bj=[bMj, bMj+1, . . . , bMj+M?2, bMj+M?1] are arranged in order. The transformation number R=2t (the initial number of t is 0) is set. The parallel bits are replaced by the transformation formula.