Table 3 Gate complexity of the proposed converter and other known converters for some similar RNSs
From: Design of reverse converters for the general RNS 3-moduli set {2k, 2n − 1, 2n + 1}
Moduli Set/Design | FA | HA/HA\(^{+1}\) | AND/OR (XOR) | Adder mod (\(2^{2n} \!-\! 1\)) | Inverters | Critical Path Delay (w/o \(d_{add\ mod\ 2^{2n}-1}\)) |
|---|---|---|---|---|---|---|
\(\{2^n, 2^n \!- \!1, 2^n \!+\! 1\}\) | n | n | n | 1 | 2n | \(d_{inv} + d_{OR} + d_{FA}\) |
Patronik and Piestrak [24] | ||||||
\(\{2^{k}, 2^n \!-\! 1, 2^n \!+\! 1\}\) | \(2n \!-\! k\!+\! 1\) | \(n+k\) | 2 | 1 | \(k+1\) | \(d_{inv} \!+\! d_{OR} + 2d_{FA}\) |
Chaves and Sousa [4] | ||||||
Version 1 | k | \(4n \!-\! \left| k\right| _{2n}\) | n | 1 | \(n+k\) | \(d_{inv}+d_{AND}+d_{CSA}(\left\lceil \frac{k}{2n}\right\rceil \!,\!1_c)\) |
(\(d_{inv} \!+\! d_{AND}\!+\!d_{FA}+d_{HA}\)) | ||||||
Version 2 | k | \(2n \!-\! \left| k\right| _{2n}\) | n | 1 | \(n+k\) | \(d_{inv}+d_{AND}+d_{CSA}(\left\lceil \frac{k}{2n}\right\rceil)\) |
(\(d_{inv} \!+\! d_{AND}\!+\!d_{FA}\)) | ||||||
Version 3 | \(k+2c\) | \(4n \!-\! \left| k \!+\! 2c\right| _{2n}\) | \(f_A(n,k)^\dag\) | 1 | \(f_I(n,k)^{\ddagger } + k\) \(^{.}\) | \(d_{inv}+d_{AND}+d_{CSA}(\left\lceil \frac{k+2c}{2n}\right\rceil \!,\!1_{c})\) |
(\(d_{inv} \!+\! d_{AND}\!+\!d_{FA}+d_{HA}\)) | ||||||
Version 4 | \(k+2c\) | \(2n \!-\! \left| k \!+\! 2c\right| _{2n}\) | \(f_A(n,k)^\dag\) | 1 | \(f_I(n,k)^{\ddagger } \!+\! k\) | \(d_{inv}+d_{AND}+d_{CSA}(\left\lceil \frac{k+2c}{2n}\right\rceil )\) |
(\(d_{inv} \!+\! d_{AND}\!+\!d_{FA}\)) | ||||||
[12] \(p=0\) | 2n | 0 | 2 (+1 XOR) | 1 | n | \(d_{FA}\) |
[12] \(p=1\) | 2n | 0 | \(n+1\) (+1 XOR) | 1 | n | \(d_{FA} + d_{OR} + d_{inv}\) |
[12] \(p > 1\) | 2n | 0 | \(n+p\) (+p XOR) | 1 | n | \(d_{FA} + d_{OR}\) |