Amplifiers with power-on trim and methods using an amplifier system having an amplifier system input and an amplifier system output, an amplifier, a comparator, a successive approximation register having an input coupled to an output of the comparator, a first switch for switching an input of the amplifier from the amplifier system input to shorting the amplifier input, a second switch for switching an output of the amplifier from the amplifier system output to an input of the comparator, an output of the successive approximation register being coupled to an N bit digital to analog (D/A) converter, the D/A converter being a non-binary converter using a radix of less than 2 for at least the most significant bits, and an output of the D/A converter being coupled to the amplifier to control the input offset of the amplifier. Novel embodiments for the amplifier, comparator and D/A converter are disclosed.