Do you know that your electronic devices light Chanukah menorahs? Not only that, they do it much more often than we do. We only light a Chanukah menorah eight days each year. They are lighting their menorahs nonstop. Here’s how:
I bet you know about gigabytes, megabytes and kilobytes but do you know what an actual “byte” is? A byte is the basic building block of all computer memory. Each byte has eight on/off switches just like our Chanukah menorahs have eight spots for candles or oil besides a place for a shamash.
Bytes work differently than the way we light our Chanukah menorahs. We just add one more light each night going from one to eight. For a computer, the switches in a byte can be flipped in all different combinations. For example on-off-on-on-off-off-on-on is one and on-on-off-off-on-on-off-off is another. Can you figure out how many possibilities there are in total?
[Hint: Start by thinking about a smaller case. For example with three switches and using 1 for on and 0 for off there are eight possibilities: 000, 001, 010, 011, 100, 101, 110, and 111]
Solution: Each of a byte’s eight switches has two possibilities: on and off. For one switch there are two possibilities. Each additional switch doubles the possibilities. That is, an added switch could be off for all of the previous possibilities or it could be on for all of them, doubling the number of previous possibilities. This means we need to calculate two times itself eight times. If you have heard of exponents, this is the same as 2 raised to the exponent 8. This number is 256.
Shabbat Shalom and Chanukah Sameach!
Ari Blinder is a math educator living in Highland Park and the owner of Math for the Masses, an innovative math tutoring and consulting company. For more information visit www.math4masses.com. Ari can be reached at [email protected].
