In the previous Halacha we have cited Maran Ha’Shulchan Aruch who rules that if one eats less than a Kezayit (twenty-seven grams) of bread, one need not wash his hands. (These twenty-seven grams of bread are calculated as if one would take bread and squash it tightly into a baby bottle such that it would reach the 27 cc mark. This amounts to approximately two-thirds of the soft part of an average slice of rye bread. One should take care not to eat exactly this amount; rather, one should eat less than this so as not to enter into a doubtful situation.)
Maran Ha’Bet Yosef quotes the Roke’ach who writes that it is uncertain whether or not one who eats less than a Kebeitza of bread is obligated to wash his hands. Thus, this individual should wash his hands without reciting a blessing.
This means that since it is uncertain whether or not one who eats less than a Kebeitza (we shall soon discuss the amount of a “Kebeitza”) of bread must wash his hands, one should therefore wash his hands without reciting a blessing so as not to recite a possible blessing in vain.
Maran Ha’Bet Yosef explains the source for this doubt, as follows: The main reason why our Sages instituted washing one’s hands before a bread meal is in order for one’s hands not to cause impurity to the food. This was something that people were careful about during the times when the Bet Hamikdash stood. The rule is that any food that does not amount to a Kebeitza does cannot become impure due to its minute size.
There is therefore room to reason that our Sages did not obligate one to wash his hands for bread which is less than a Kebeitza. On the other hand, it is possible that our Sages did not differentiate between bread which amounts to more than a Kebeitza or less than one.
Thus, halachically speaking, Maran Ha’Shulchan Aruch rules that one who eats less than a Kebeitza of bread must wash his hands but must not recite the “Al Netilat Yadayim” blessing.
Maran Rabbeinu Ovadia Yosef zt”l discusses the amount of a Kebeitza in this context in his Halichot Olam, Volume 1, page 316. Halachically speaking, he rules that one who eats up to fifty grams of bread should wash his hands without a blessing (for in this context, a Kebeitza is measured as an egg without its shell which weighs less than an egg with its shell, i.e. fifty-four grams).
Summary: One who eats less than fifty grams of bread (but more than twenty-seven grams) must wash his hands without reciting a blessing. Only when one eats more than fifty grams of bread must one wash his hands and recite the “Al Netilat Yadayim” blessing.