The Biblical Commandment of Birkat HaMazon
According to the opinion of Chachamim, one only recites Birkat HaMazon upon eating bread (see Mishna, Berachot 44a and Rashi ad loc.). The Mishna, Berachot 45a, records a dispute regarding the amount of bread one must eat in order to recite zimun (the joint Birkat HaMazon performed when three people eat together). One opinion is that the minimum amount is a k'zayit (the size of an olive). The other opinion is that the minimum amount is a k'beitzah (the size of an egg). The Gemara, Berachot 49b, explains that the dispute is contingent on the interpretation of the verse "v'achalta v'savata" (and you shall eat and be satisfied), that is mentioned in conjunction with the mitzvah of Birkat HaMazon. The opinion that maintains that the minimum amount is a k'zayit interprets "and you shall eat" as referring to eating a k'zayit (k'zayit is the standard size for any mitzvah or transgression that involves eating something); "and be satisfied" refers to the requirement to drink in addition to eating. [See also, Ramban, Berachot 49b, who interprets this opinion to mean that one is obligated to recite Birkat HaMazon if he eats bread or drinks wine.] The opinion that maintains that the minimum requirement is a k'beitzah interprets "and you shall eat" as referring to eating a k'zayit; "and be satisfied" teaches that it is not enough to eat a k'zayit but a k'beitzah.
The implication of the Gemara is that there is a biblical obligation to recite Birkat HaMazon either by eating a k'zayit and drinking something or by eating a k'beitzah (depending on which opinion one follows). However, there is a passage in the Gemara, Berachot 20b, which records a conversation between the Almighty and the Angels in which the Almighty praises the Jewish People for going above and beyond the call of duty. "I wrote in the Torah 'and you shall eat and be satisfied and bless the Lord for the land that he has given you' and they are meticulous (to recite Birkat HaMazon) on a k'zayit and a k'beitzah." The implication of this passage is that the biblical obligation to recite Birkat HaMazon only applies if one is actually satisfied and recitation of Birkat HaMazon upon eating k'zayit and k'beitzah is considered volunteerism (based on a rabbinic enactment).
The Rishonim have two basic approaches to resolve the apparent discrepancy. Tosafot, Berachot 49b, s.v. Rabbi Meir, cite Rabbeinu Yitzchak who suggests that the biblical commandment to recite Birkat HaMazon only applies if one is fully satisfied from his meal. The amounts of k'zayit and k'beitzah are not of a biblical nature, but rather of a rabbinic nature. The prooftexts brought to support the amounts of k'zayit and k'beitzah are not bona fide proofs, but rather hints in the text (asmachta). Rashba, Berachot 48a, s.v. Ha, on the other hand, is of the opinion that the two passages in the Gemara reflect conflicting opinions among the Amoraim as to whether the biblical amount for Birkat HaMazon is k'zayit/k'beitzah or whether it is full satisfaction. Rashba rules that the normative opinion is the opinion that k'zayit (and a drink) is the biblical amount for Birkat HaMazon.
Mishna Berurah 184:22, rules in accordance with the opinion of Tosafot that one is only obligated to recite Birkat HaMazon on a biblical level if he ate enough to be fully satisfied. Nevertheless, the opinion of Rashba is not totally rejected. Rama, Orach Chaim 197:4 (based on Mordechai, Berachot no. 177), rules that when one is choosing who should lead the zimun, it is preferable to choose someone who drank something at the meal. The reason for this ruling is that according to the opinion of Rashba, there is no biblical obligation of Birkat HaMazon unless someone ate a k'zayit and drank something. In choosing a leader for the zimun, someone who is biblically obligated takes precedence over someone whose obligation is rabbinic. Mishna Berurah 197:28, notes that if someone ate to full satisfaction but didn't drink and another did not eat to satisfaction but drank, the one who ate to satisfaction would take precedence because the opinion of Tosafot is the primary opinion and the opinion of Rashba (and Mordechai) is an added stringency.
The Significance of a Biblical Obligation
The distinction between the biblical obligation of Birkat HaMazon and the rabbinic obligation has certain practical ramifications. First, Rambam, Hilchot Berachot 2:14, rules that if one ate and is unsure whether he recited Birkat HaMazon, he should repeat Birkat HaMazon. Shulchan Aruch, Orach Chaim 184:4, codifies the opinion of Rambam and explains that the reason why one must repeat Birkat HaMazon is because Birkat HaMazon is a biblical commandment (and regarding biblical commandments one must be stringent in cases of doubt). Mishna Berurah 184:15, adds that this ruling only applies if one was fully satisfied from his meal. If he was not fully satisfied, he is not biblically obligated and he should not repeat Birkat HaMazon.
Second, Mishna Berurah, Biur Halacha 184:6, rules that if one eats bread and then eats other non-bread foods and becomes satisfied, he is biblically obligated to recite Birkat HaMazon. He then presents a novel extension of this ruling. If someone eats (at least) a k'zayit of bread and is not satisfied, he is obligated to recite Birkat HaMazon on a rabbinic level. Suppose he then eats non-bread items after reciting Birkat HaMazon and becomes fully satisfied. Mishna Berurah suggests that since his satisfaction is due to a combination of the bread that he ate and the other foods and the Birkat HaMazon that he previously recited was insignificant on a biblical level, he must repeat Birkat HaMazon.
Chazon Ish, Orach Chaim 34:4, disagrees with Mishna Berurah's suggestion. He claims that although the Birkat HaMazon recited prior to satisfaction has no significance on a biblical level, it does have significance on a practical level. According to Chazon Ish the rabbinic Birkat HaMazon serves to disconnect the bread portion of the meal from the non-bread portion of the meal such that it is considered as two different meals on a biblical level. Non-bread items are only included if they are eaten in the same meal as the bread.
The Role of "V'Achalta"
Normally, eating to full satisfaction will include eating a k'zayit of bread. Nevertheless, if non-food items are included in the calculation, it is possible to construct a case where one eats a small amount of food and then becomes fully satisfied from non-bread foods. Determining whether one is obligated to recite Birkat HaMazon in this case would depend on how one interprets the verse "v'achalta v'savata." If the obligation of Birkat HaMazon is both v'achalta and v'savata, then unless one eats a k'zayit (v'achalta) and one is fully satisfied (v'savata) there is no biblical obligation of Birkat HaMazon. However, one can suggest that the primary obligation to recite Birkat HaMazon is full satisfaction, and the reason why the Torah uses the term v'achalta is because that is the normal way to reach full satisfaction. As such, one would recite Birkat HaMazon if one eats less than a k'zayit of bread and reaches full satisfaction by eating non-bread foods. P'ri Megadim, Eshel Avraham 210:1, suggests that in such a situation one should recite Birkat HaMazon.
The role of the term "v'achlata" is also relevant to a question raised by R. Akiva Eger, Hagahot R. Akiva Eger, Shulchan Aruch, Orach Chaim 286:2. R. Eger discusses a case of a minor who eats to full satisfaction, recites Birkat HaMazon and then becomes a bar mitzvah while he is still satisfied. R. Eger wonders whether he should repeat Birkat HaMazon being that the Birkat HaMazon recited while he was a minor was insignificant on a Torah level. He notes that the question is contingent on the role of the eating process in the obligation of Birkat HaMazon. If eating is significant (i.e. v'achalta is a necessary component in obligating someone to recite Birkat HaMazon), eating as minor would not re-obligate him in Birkat HaMazon as an adult. If, however, the primary obligation to recite Birkat HaMazon is full satisfaction, he would be required to repeat Birkat HaMazon as he is currently satisfied and the previous Birkat HaMazon was insignificant on a Torah level. R. Eger writes that he is unsure how to rule on the matter.