Thu, 12 Sep 2013, 03:32

Three students, two after class, one later in my office, all had the same question about the MASK in my bit vector example. So, I thought an email message to you would be a good idea. Recall in class we used a bit vector P1 P2 P3 P4 P5 P6 to represent which of six printers are available to send a file to for printing. There are 2^6 possible printer situations, and each can be described by one of the 2^6 possible bit vectors. Each Pi represents a printer that is either idle or busy. If Pi=0, the printer is busy. If Pi=1, the printer is free. If the bit vector is 010001, printers 2 and 6 are free (Pi=1) and printers 1,3,4, and 5 are busy (Pi=0). Recall we decided to send the file to Printer 2. After sending the file to Printer 2, we want to indicate that Printer 2 is also now busy. We do that by changing P2 from a 1 to a 0. I suggested ANDing 010001 with the MASK 101111. And, sure enough it works! Three students pointed out later that it will also work for the MASK 000001, that is, we will get the same result if we use the mask 000001. That is true, the mask 000001 will work for the bit vector 010001. But that mask will not work for the bit vector 110001, for example. Do you see why it won't work for bit vector 110001? I suppose we could pick our mask depending on the bit vector, but that would be cumbersome. Much better if we can have ONE mask that will work on all 2^k bit vectors. That is, one mask that will change P2 from 1 to 0 and leave all the other bits alone, regardless of the bit vector. How do we accomplish that? The MASK is M1 M2 M3 M4 M5 M6 We want the mask bits to leave alone all the Pi bits EXCEPT P2, the one we want to make 0. ANDing the bit vector with the MASK independently ANDs each Pi with its corresponding Mi. If M2=0, the result of ANDing P2 and 0 is 0. If all the other Mi=1, we have Pi AND 1 for all the other bits. The result is 1 if Pi=1, and 0 if Pi=0. The ONE MASK 101111 works for all bit vectors. Now the Flip side: ================= Now the flip side: Making P5 go from 0 to 1 to reflect the fact that printer 5 is now done printing and is now available for another job. If we OR the bit vector with the MASK, we need a MASK that keeps all Pi except P5 the same and makes P5=1. How do we do this? That is, what ONE mask will work on all bit vectors. We use the OR function. Pi OR 0 is Pi. P5 OR 1 is 1. Therefore the MASK for setting P5 and leaving all other Pi unchanged is 000010. And, this one mask works for all situations, that is, for all 2^6 bit vectors. Hope this helps. See you in class on Monday. Yale Patt