Bitmasking and bitwise
operations are low level programming techniques used for turning bits off and
on - the manipulation of bits provides a way to make representations in a
computer. The goal of bitmasking in SQL Server 2005 is to combine two or more
attributes, normally stored into a single column in a table, into one
hexadecimal value to make representations as well. Achieving this goal has many
possibilities, as we will discover later, and introduces many computer science
concepts into the relational database. Part 1 of this series is an introduction
to counting and bitmasking in SQL Server. In Part 2, we will discover its
practical application in SQL Server. Finally, in Part 3, we will explore
programmability using bitmasking techniques.
Why Bitmask?
Suppose,
for instance, that you have been assigned to capture 50 Request.Browser
properties (Figure 1) from your website and maybe 50 keys in the Request.ServerVariables
collection off of the web to store in SQL Server. Are you going to create 100
columns in a table to hold these values? Sure, you can and that will work very
well, but bitmasking several values to one value is a cleaner, neater, and more
efficient approach in my opinion.
Figure 1 : A Request.Browser property (c#)
Figure 1 shows one of many
different attributes that you can pluck out of a user's visit to a website,
important information that many companies capture. Here, a web developer writes
code to capture the Boolean value of a browser's cookie status. Before we get
into an example, we must review numbers, counting, base 10, base 2, and
hexadecimal notation.
(If you are already familiar
with these concepts, please skip this part). You will need to understand these
terms and associated techniques to begin masking multiple values to single
values.
A Review of Bits, Numbers and Counting
The basic and lowest level
of a computer's representation of anything is a bit. A bit has two values as
most of us know on and off. While you expected me to say 1 and 0, one only
has to look at a half a dozen different ANSI applications to find that on and
off are represented a half dozen different ways. For this article, we will use
0 and 1; don't be surprised, however, to find other values, highly inconsistent
might I add, even in platforms and applications that are written by the same
company, no less. Generally speaking, we associate 1 to be equal to on; 0 to
represent off, but if you wanted to you could reverse this representation I
suppose. Table 1 defines a table for some of our terminology. Four bits are a
nibble and two nibbles are a byte. A WORD is 2 bytes, or 16 bits, and 32 bits
are a DWORD. A nibble will be a very important term to grasp as we begin
mapping bits.
Table 1 :Bit terminology
Numbers can be represented
via a series of bits in combinations that are either on or off. Your computer
represents things as numbers as well, such as memory locations, printer ports,
devices, etc. When you think about it in this context, we can certainly represent
things with numbers of our choosing if we are inclined to in the relational
database - permissions, cities, states, hair color, gender can be assigned a
numerical value. And by doing such, we are representing entities, objects,
or things just as your computer does. Let us now look at Base 10 and Base 2
notation. This will allow us to become acquainted with numbers and their
representations. We'll first pick an easy number, and then a larger one as our
working examples. If you remember from mathematics, our numbering system is centered
on the Decimal System, or Base 10. Let's look at some Base 10 representations
of our numbering system. Understanding the following is critical to bitmasking
in SQL Server 2005.
Base 10
Check out Table 2 for a
refresher on simple Base 10 counting. We will build off of this concept later. Remember
that we can count numbers in a variety of ways. Follow each line in the
graphical representation to get (re)acquainted with counting numbers in this
manner. At this point, a calculator might be handy to verify some of what I am
deriving.
Table 2 : Counting numbers with Base 10
We certainly could have expanded line 11 in our table even further, but I think you get the point. The number 10 is the base value of our final calculation here, and we can express final results based on 10 raised to a power times another value.
Base 2
As Base 10 is synonymous with the Decimal system, so is Base 2 to the Binary System.
Because bits are used to represent numbers in a computer, we find it easier to translate our numbering to bit notation (we previously pointed out that the core of computing is based on only two values). Rather than using Base 10, we will use a Base 2, as it provides to us a much easier way to represent our values.
A very important concept, Base 2 allows us to translate from hexadecimal to decimal and back very easily. Mapping values using base two is much easier than trying to keep up with counting all of the zeroes and ones when using Base 10.
Table 3 : Base2 mapping
The above table first shows us that one nibble and one byte, all zeros, has a value of zero. A byte, all 1's (all bits turned on) has a value of 255. How did we come up with this?
1 1 1 1 1
1 1 1
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
=255
+ + +
+ + +
128 64 32 16 8 4 2 1 =255
+ + +
+ + +
240
15 = 255
Let's break this down piece
by piece. Don't worry all of this will come together for you soon. Each bit
position represents an ordinal position within a byte. Starting from right to left
(we could have started from left to right it's personal preference), position
0 is represented by two to the zero power, which equals one. Moving to the left
one position, we find two to the first power, or 2^ 1, which gives us the value
of two. (Notice the increasing value of the exponent by one, starting at zero, each
iteration). Again using base two, our Base 2 value next is raised to the
second power, and then two raised to the third power, etc. Since all the bits
are on in the first nibble of this byte, what is the value of the sum of the
first four numbers? Fifteen, you are correct!
Now let's examine our value
of 15 further, and place it in our windows scientific calculator. Make sure
that you enter 15 and that it is reading in Dec, short for decimal notation.
Now, change it to Hex, short for Hexadecimal notation. What the heck? Our value
is F. Where did this come from? Remember that our visual representation is
easily changed to Hex from Base 2.
Display 1 : Our value 15 as Hexadecimal
Review Table 4. This mapping allows us to successfully convert our numbering scheme from base two to Hex notation. This final representation of numbers is what we will actually use in our masking far easier than trying to convert base 10 or base 2 to something visual that we can work with.
Decimal | Bin | Hex |
0 | 0000 | 0 |
1 | 0001 | 1 |
2 | 0010 | 2 |
3 | 0011 | 3 |
4 | 0100 | 4 |
5 | 0101 | 5 |
6 | 0110 | 6 |
7 | 0111 | 7 |
8 | 1000 | 8 |
9 | 1001 | 9 |
10 | 1010 | A |
11 | 1011 | B |
12 | 1100 | C |
13 | 1101 | D |
14 | 1110 | E |
15 | 1111 | F |
Table 4 : A conversion table for bits
Study this concept for a moment, and try to come up with some values of your own. For practice, jot down a few numbers between 0 and 20 and try to figure out their binary value
representation.
Let's look at another example, this one is more difficult. Let's attempt to map the hex value of our previous, 4458. Before we can do this, we have to calculate its value in Base2. We must first figure out how to get there. Here is what I come up with:
4458 = 2^12 + 2^8 + 2^6 + 2^5 + 2^3 + 2^1
= 4096 + 256 + 64 + 32 + 8 + 2
If we now map each nibble, we end up with the following:
Notice how each set of 4 bits translates nicely into our first beginning value of Base2 exponential notation. Let's look at it again:
We treat each nibble as if they were stand alone the first nibble is the sum of 2 + 8, since the second and forth bits are on, giving us a value of 10 (or the value A!). For the second nibble, the second and third bits are on, summing to give a value of.6(2 + 4). Yes you got it! Revisiting our scientific calculator, we see that our numbers appear to be correct.
Display 2 : Our number 4458 as Hex and Dec
Again, review this concept carefully before moving on. Pick a few numbers larger than, say, 100, and come up with 1) its binary representation and 2) its hex representation. Understanding this exercise, converting from decimal to binary to hexadecimal, is critical to successful bitmasking. Let's now begin with a fictitious problem and solve it via bitmasking.
Our Problem
Given
our refresher, we are ready for a challenge. We have been tasked to bitmask 3
values that are generated each time a visitor comes to our website. We are to
record 1) the operating system, 2) the browser used, and 3) whether or not
cookies are turned on in the client environment. We wish to combine these three
values into 1 bitmasked value and store this in the database.
Preparing to code our mask
Before
we begin coding T-SQL, I first find it easy to mask values into a single value
by creating a key, or legend, that will guide me to the correct bit placement
of my values. Below is a useful way to prepare a legend as a map to 1) Define the
number of bytes needed, 2) Keep track/calculate bit values, and 3) Position of
the bytes where you wish to store your values. Simply add one of these as a
comment in your code so that you have a reference to go back whenever you like
to remind yourself of the mask positions for your values. Examine the key in
Figure 1 and study the explanation of the key carefully.
Figure 2 : Creating a key to map bitmask values
Explanation of the key
In our example, we will use only 1 byte to represent three columns. (If you were masking several columns, you
would need more bytes for storage). First, I assign the placeholders for the
bit values: 2 bits for the operating system, 3 bits for the browser type, and 1
bit to notify if cookies are turned on or off. The second portion of the key
outlines the assignment for your mask. We are using 1 byte which has 8 bit
positions. Each position will be assigned bit values. For O (operating
system), I previously defined in the key that we will allow three values, so
I'll need 2 bytes. For Browser B storage, I'll need 3 bits (Remember why 3
bits allows for 7 storage values? If you forgot, go back and review counting
numbers. You'll get it!), and for Cookie C values just 1 bit. Note that I map
them in the Mask line above, each of the 6 bits that I'm using assigned to a
corresponding value for my mask. This is very important, since you will actually
be placing numerical representations of your data within these bits. It does
not matter than I do not use all 8 bits that I have allocated in our example
we can leave the remaining bits zero without disrupting our storage or
retrieval process.
Coding the Mask
Below is the code that will mask our values. Review this script, and then look a the explanation below.
Figure 3 : Code to mask our data into one value
Lets briefly review the above steps for coding the mask.
Steps to mask values
Step 1) Binary data type
at this point, you choose the binary or varbinary data type that you will use.
The more values that you have, the larger the data type necessary to store
values. I use a varbinary (1) data type for no reason other than I normally use varbinary instead of binary (length 1 doesn't vary, obviously).
Step 2) Assign Mask Values values that we wish to mask. They could come from
a web page, a rich client, web service, or whatever. For this initial demo, we're
just running a script, so hard-coded values are adequate.
Step 3) Assign the shift values these variables store the multiplier to allow
you to shift, within the byte or bytes, the beginning point for you storage
attributes. For example, the first variable, @BitshiftBrowser=4, will allow us to skip the first two bits (our
designated holding spot for the operating system) in order to get to the location
where we are going to store our browser settings.
Step 4) Assign code to values in order to store our values, remember back to
our previous paragraph on object representations in the computer. Here we
simply assign a number to our value via the CASE
statement.
Step 5) Mask the values use the bitwise OR operator to place the integer
value that represents our textual value inside of the binary data type at the
outlined location. (For further reading, see http://en.wikipedia.org/wiki/Bitwise_OR#OR).
Step 6) Masked value our end result. We have successfully collapsed 3 attributes into 1 value (Figure 3); we could have put hundreds of them into one value. A powerful concept? I agree!
Figure 4 :Bitmasked value final result
Decoding the Mask
Just as we code the mask, similarly we must decode the hexadecimal value (Figure 5). Let's look at the steps to accomplish this.
Figure 5 : Decode the masked value
Steps to decode mask values
Step 1) Unmask value using
integer representation This is a simple decode. The values that you
previously assigned to your textual representation are reversed. For the first
bit, you perform a bitwise AND (http://en.wikipedia.org/wiki/Bitwise_AND#AND)
to recapture the values.
Step 2) Shift using & and division As we shifted to the right to place the
values into the mask, we must divide by the same bitshift variable to decode
the second and subsequent values out of the mask. The mask value/shift integer anded
with the storage value assigned in the code mask steps is found again by the CASE statement.
Step 3) Display final result
Figure 6 : Final decoded value
Conclusion
Bitmasking in SQL Server is fun, powerful, and a neat way to store data in a relational database. While it shouldn't be used to overpower or overcomplicate solving a particular task, as it is with every tool in our SQL Server toolkit arsenal, there is a time and a place for everything. Keep this technique in mind next time you have to store many attributes into a table. In Part 2, we will look at how you might build objects in the database that will allow implementation of this concept. We'll also look at some queries and indexing the bitmasked value, and look at performance implications for a bitmasked value in SQL Server.
About the Author
Lee Everest is a Sr. Consultant for Software Architects, and a part-time SQL instructor at North Lake College in Irving, Texas. He can be reached at tsql-northlake@dcccd.edu