BER formula

i am trying to calculate the BER for an ADC, but all what i can find online is that formula, which seems not accurate at all
BER = number of error/ total no. of bits sent
i will compare between two scenarios

sent-------0 0 0 0 0 0 1
received--0 0 0 0 0 0 0

sent-------1 0 0 0 0 0 0
received--0 0 0 0 0 0 0

in both cases the BER is 0.2 or 20%. in example one the error is insignificant as the error is on LSB and can be easily ignored. in example two the error occurs on MSB bit which makes the whole information different. in both cases, the formula says there are two errors, without mentioning which bits are damaged.
is there another formula which can be more accurate i can use??
any help would be greatly appreciated,
Mohamed abu helala,

If you know something about the signal, you might define the range of the next value expected.
could that be a strategy?

The concept of "bit error rate" applies to methods of data transmission, not to a device like an ADC.

sent-------0 0 0 0 0 0 1
received--0 0 0 0 0 0 0

As jremington says, BER is applicable to data transmission.

When referring to an ADC, what do you mean by "sent" and how do you know what was sent?