Design of Reversible Decoder with minimum Garbage Output

Abstract

Reversible logic is helpful in designing low power applications. Many reversible gates have been introduced in recent time for use in reversible computing. Those gates are used in the design of various circuits. In some works, decoders using reversible logic have been also proposed. This paper proposes three new reversible gates that can perform multiple logical operations alone. Using these gates, new circuits for 2-to-4 and 3-to-8 decoders are proposed followed by two new designs for general decoder. The performances of the proposed decoder circuits are studied in terms of hardware complexity, power, gate count, number of ancilla inputs and garbage outputs. Comparisons of these circuits with similar existing decoder circuits are also presented. The proposed circuits are found to have better performance characteristics particularly garbage output is least amongst available designs.

Optimized Design of Decoder 2 to 4, 3 to 8 and n to 2n using Reversible Gates

“…6) RI Gate : A reversible gate 3 * 3 having for inputs A, B and C as outputs P = B, Q = AB'+BC C and R = AB C the quantum cost of the RI gate is equal to QC = 4, its Hardware complexity is worth HC = 1 α+3β+1δ [8] 9) TR Gate : A reversible gate 3 * 3 having for inputs A, B and C as outputs P = A, Q = A B, R = AB' C, S = AB C bigoplus D the quantum cost of the TR gate is equal to QC = 4 and its Hardware complexity is equal to HC = 2 α + 1 β+1 δ [20] 10)DVSM Gate : A reversible gate 4 * 4 having for inputs A, B, C and D as outputs P = AB A'C, Q = AB' A'C, R = A'B AC'and S= D AC A'B' the quantum cost of the TR gate is equal to QC = 11 and its Hardware complexity is equal to HC = 5 α + 7 β+3 δ [11] 11)MFRG1 Gate : A reversible gate 3 * 3 having for inputs A, B and C as outputs P = A, Q = A'B AC', R = A'C AB, the quantum cost of the TR gate is equal to QC = 4 and its Hardware complexity is equal to HC = 2 α + 4 β+2 δ [12] 12)MFRG2 Gate : A reversible gate 3 * 3 having for inputs A, B and C as outputs P = A', Q = A'B AC, R = A'C AB, the quantum cost of the TR gate is equal to QC = 4 and its Hardware complexity is equal to HC = 2 α + 4 β+1 δ [12] 13) OM Gate : A reversible gate 3 * 3 having for inputs A, Band C as outputs P = A, Q = AB C', R = A'B C',the quantum cost of the OM gate is not mentioned in the literature and its hardware complexity is HC = 2 α + 2 β+2 δ [13] 14) SOM Gate : A reversible gate 4 *4 having for inputs A, B, C and D as outputs P = AB C D, Q = AB' C, R = A'B C D S=A'B' C D,the quantum cost of the SOM gate is not mentioned in the literature and its hardware complexity is HC = 5 α + 4 β+2 δ [13] 15) UM Gate : A reversible gate 6 *6 having for inputs A, B, C ,D,E and F as outputs P = A, Q = AB C', R = A'B C' S=A D, T=DE F' and U=D'E F' the quantum cost of the SOM gate is not mentioned in the literature and its hardware complexity is HC = 5 α + 4 β+4 δ [13] 16)RD Gate : A reversible gate 4 *4 having for inputs A, B, C and D as outputs P = AB D, Q = (A+B)' D, R = (A+B') C D S=AB' D, the quantum cost of the RD gate is 8 and its hardware complexity is HC = 5 α + 2 β+2 δ…”

“…A. Decoder 2 to 4 1) Design1 & Design2: In 2020 Gunajit Kalita [13] proposed 2 decoders designs 2 to 4 as shown in Fig. 1 and 2, respectively .…”

“…In this paragraph we will present our circuits concerning the decoder 2 to 4, 3 to 8 and n to 2 n Our work is based on the article [13] ,we try to modify it to improve certain performance criteria, starting with:…”

“…We thought of exploiting its circuit 2 to 4 [13] by replacing the reversible gate SOM by that of the RD and to assign to the third and fourth input the value 0 Fig. 31 shows our design of decoder 2 to 4.…”

“…In the 3 r d section, we exploit a design of each decoder 2 to 4, 3 to 8, and n to 2 n from a recent article [13] we modify and show their associated performance criteria. To compare our new designs, we expose several designs from previous studies for comparison against our new designs of each decoder in terms of the 5 performance criteria CG, NGO; NCI, QC, and HC.…”