Quick Test of an ADC

I have an 8BIT MAX160 Analog Digital converter I am using in several boards. I was wondering if there was a way to quickly test the accuracy of the ADC and output range of the ADC to verify bit errors, etc.

My idea was to increase the incoming analog signal one bit "count" in magnitude for each iteration in a loop:

ADC Input range 0 - 4.00 VDC

calculated mV/Count: 0.015625

Example:

Analog Input (VDC)      Expected Output

0.00            00000000
0.015625        00000001

0.03125         00000010
0.0625          00000100
0.125           00001000
0.25            00010000
0.50            00100000
1.00            01000000
2.00            10000000
4.00            11111111

Test method:

Start at 0VDC to see if any "stuck" bits/lines are present.

Do a "walking 1" for each successive magnitude bit position

Then do 4.0 Max input for All 1's

My question is, would this be a valid "quick" test to run an ADC through, instead of doing every possible input value from 0 to 255?