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Reversible circuits, nowadays, have found grounds in many applications such as low power CMOS design and quantum computing. In reversible circuit design, decreasing three parameters is of interest: quantum cost, depth of the circuit and the number of garbage outputs. On the other hand, recently, decimal computer arithmetic, for the sake of its preciseness, gains popularity. Given that the BCD digit adder is the basic unit in decimal arithmetic, in this paper we propose a new reversible design for this unit with the aim of minimizing the depth of the circuit. Furthermore, we show that the proposed designing method can be applied to any other reversible circuit for reaching the minimum depth.