A random estimation analog-to-digital converter for converting a first analog signal into a digital signal includes a random bit generator, a digital-to-analog converter, a summer, an M-bit analog-to-digital converter, and a digital combiner. The random bit generator generates random least significant bits (LSBs) and the digital-to-analog converter then converts the random LSBs into a second analog signal. The summer subtracts the second analog signal from the first analog signal in the analog domain. The M-bit analog-to-digital converter then converts the modified first analog signal into the most significant bits (MSBs) of the digital image signal. The digital combiner combines the random LSBs with the MSBs in the digital domain to generate the digital signal. In one example, the random LSBs are extra bits that are beyond the maximum resolution of the M-bit analog-to-digital converter.