33.1.7.1 Sign/Magnitude and Two’s Complement Result

In sign/magnitude format, the conversion result is a binary representation of the input, with a sign bit determining the polarity. Equation 33-3 can be used to calculate the full-scale range of ADC result values in sign/magnitude format:

$$\begin{gathered} n-bitrangeinsign/magnitudeformat=\pm 2^{n-1}-1 \\ where: \\ n=ADCresolution \\ Examples: \\ 12-bitADC=\pm 2^{12-1}-1=\pm 2047 \end{gathered}$$

In 12-Bit Sign/Magnitude Result Format, the right justified ADRES value is ’0x8020’. The 11-bit sign/magnitude formatted result shows an absolute value of ‘2’ (decimal), with bit 7 of the ADRESH register representing the sign bit. When the sign bit = ‘0’, the result is positive, and when the sign bit = ‘1’, the result is negative. For this example, the sign bit = ‘1’, so the sign/magnitude formatted decimal result value is ‘-2’.

In two’s complement format, the MSb of the conversion result determines the polarity. Equation 33-4 can be used to calculate the full-scale range of ADC result values in two’s complement format:

$$\begin{gathered} n-bitrangeintwo\prime scomplementformat=(-2^{n-1}-1),(2^{n-1}-2) \\ where: \\ n=ADCresolution \\ Example: \\ 12-bitADC=(-2^{12-1}-1)=-2047(lowrange) \\ =(2^{12-1}-2)=2046(highrange) \end{gathered}$$

In 12-Bit Two’s Complement Result Format, the right justified ADRES result is ’0x8020’, which matches the ADRES result in 12-Bit Sign/Magnitude Result Format. The 12-bit two’s complement result shows a value of ’-2046’ (decimal), with bit 7 of the ADRESH register representing the MSb of the conversion result.