Adder based residue to binary number converters for (2ⁿ - 1, 2ⁿ, 2ⁿ + 1)

Based on an algorithm derived from the New Chinese Remainder Theorem I, we present three new residue-to-binary converters for the residue number system (2ⁿ - 1, 2ⁿ, 2ⁿ + 1) designed using 2n-bit or n-bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2n-bit adder based converter is faster and requires about half the hardware required by previous methods. For n-bit adder-based implementations, one new converter is twice as fast as the previous method using a similar amount of hardware, whereas another new converter achieves improvement in either speed, area, or dynamic range compared with previous converters.