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The ADC0808’s data sheet states clearly that the input range is 0V to 5V so anything that fits into this range is all right ..
If you have ac voltage (with no dc offset) and you want to use the ADC0808 to measure it you have to add 2.5V dc offset and then the maximum amplitude of this signal is 2.5V (or 5Vpp) ..
all the adc's convert the input voltage aquired when it receives the conversion command, to a digital value. there's no question of ac or dc
in case of ac also, at the time when the adc "take" the input voltage, it will be at a specific voltage level.so it will convert that voltage to binary.
also as IanP said it depends on the vref also, according to which the adc determines the minimum and maximum value of input voltage
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