
Shabbat Parashat Shemini 5765Ask the RabbiQuestion: This sounds like a crazy question, but what is the halachic ruling on one who counts sefirat haomer in a base other than the standard, decimal system?In other words, could he say, “Today is 1101 in base 2” on day 13.
Answer: From a practical perspective, this does seem like a crazy question, but trying to answer it gives us the opportunity to more clearly define how one performs the mitzva of counting. When it might be practical is when one is asked the day of the omer before fulfilling his mitzva. Instead of telling what the count was yesterday, one might want to answer with the day’s count in a different base if that is not a valid way of counting (see Shulchan Aruch, Orach Chayim 489:4).
One can demonstrate from the Shulchan Aruch (ibid.) that one does not fulfill the mitzva of sefirat haomer by stating information that makes it clear what day of the omer it is. Otherwise, saying yesterday’s date would be like saying today’s date. Thus, one has to say something relatively direct about the number that corresponds to the day in the omer. But how formal does it have to be?
Firstly, the poskim understand as a simple matter that one can do sefirat haomer in any language he understands (Magen Avraham 489:2) and some say that one does not fulfill the mitzva if he does not understand, even in Hebrew (ibid.). So one can say that the important thing is getting the point across in reference to the day’s count. If so, what difference does it make if it is in done in a different language or in binary. In fact, many Acharonim (see Sha’arei Teshuva 489:6; Biur Halacha, on 489:1; Kaf Hachayim 489:24) dispute or have doubt as to whether or not one fulfills the mitzva by saying the number in gematria form (e.g. “yud gimmel” for 13). One might claim that the answer to your question depends on that dispute, as all numerical systems are probably the same. Furthermore, the Ba’er Heitev (:6) says that one fulfills the mitzva by saying “arbaim chaser echad (40 minus 1)” for the 39^{th} day, dipping further into arithmetic computations.
However, there is great logic to distinguish between your case and the aforementioned. It is true that our definition of what a number is may be broad enough to include gematria. But gematria is at least a normal way for many people to express numbers. In Talmudic Hebrew, “40 minus 1” is also a catch phrase for 39 (see Shabbat 73a). (One can, therefore, take issue on the B’er Moshe (III, 82) who simply equates “5 minus 1” to “40 minus 1.”). In contrast, talking in binary is not normal in any language (if one, properly, excludes computer languages).
The matter may depend on the careful reading of earlier sources. The Tur (OC 489) cites the Ra’avyah’s opinion that when one is in between multiples of 7 days he doesn’t say the number of days but, for example, “a week and 6 days” for 13. A week is an accepted way of saying 7 days and it seems to be equivalent to the gematria case. Yet, the Tur feels compelled to explain that this is valid because on day #7, he said, “7 days, which is a week.” The Chok Yaakov (489:8) says, in fact, that if on day #7 one says just “a week” the Ra’avyah agrees that he does not fulfill the mitzva. Only after formally stating in our counting that 7 days is equivalent to a week are they interchangeable. (Some argue on the Chok Yaakov and one can also say that the Tur’s explanation is needed only to explains why the Ra’avyah’s system is legitimate l’chatchila, whereas, you are likely interested in the ruling, b’dieved).
In the final analysis, if counting in gematria is invalid,then bases other than decimal are certainly invalid. If one accepts gematria, then there is a possibility to discuss binary. However, logic still dictates that one must express the count in a numerical system which is readily used in the language one is using.
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