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Bit Manipulation

Bit manipulation represents the elegant and concise facet of algorithms. Apparently, it is based on how the computer stores the information. With such down-to-the-bottom level data structures or operations, the space usage is usually the minimum. The least usage of space makes the speed fast as well.

The unit is bit, which only has two possible values, 0 or 1 (which is exactly the reason that the base is 2, or binary). For the integer data type (int) in most computer system nowadays, there are 32 bits. 

Byte is different from bit. Each byte has 8 bits (so one integer has 4 bytes in size). Thus, the value range of a byte is in [0, 2^8 = 256) (if you know ACII code before, have you ever ask why the range is [0, 256)?). This connects to some very common words used daily,

 1 KB is (2^10 = 1024 ~ 10^3) byte

 1 MB is (2^10 = 1024 ~ 10^3) KB

 1 GB is (2^10 = 1024 ~ 10^3) MB

 1 TB is (2^10 = 1024 ~ 10^3) GB

If we have an integer array with a size of 10^6, the total size is 4*10^6 ~ 4 MB. If you have a movie which is about 100 GB in size, the number of bits in it can also be estimated (homework...).

Now let move on to the negative numbers, which is related to signed numbers. For the signed numbers, the bit on the most left is the flag bit. When it is 0, it is non-negative; when it is 1. it is a negative number. Thus, for the signed integer, the range is [-2^31, 2^31), or

INT_MIN = -2^31

INT_MAX = 2^31 - 1

If you look at the bits of INT_MAX, they are 0111...111, or one 0 + thirty-one 1's;

Then how about INT_MIN?

If this is the first time for you to think about this question, you may guess it may be thirty-two 1's. But actually it is not. It is 1000...000, or one 1 + thirty-one 0's. I know you may ask:

1. why?

2. if this is true, then what is the number with all bits of 1?

The first question is very good one, but I will not try to answer the question here, since it does involve some design logic back to old days of computer. There are good resources online about this. 

For the second question, the answer is -1. (What?) Such a fun world! isn't it?

The next topic is bit-wise operations. The common ones are: & (and), | (or), ^ (xor),  ~ (opposite or NOT), >> (left shift), and <<(rigth shift).

Besides the definitions, pay attention to the precedence of these operators. This will cause some hidden bugs in code if not handle correctly.

Finally we can go to the applications in coding! Yeahhh


Question List


Upper Layer


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