Bit Manipulation
Bit manipulation means directly performing operations on bits using operators such as AND, OR, XOR, NOT, and bit shifts. It is widely used in low-level programming, embedded systems, and performance-critical applications. By directly manipulating bits, we can represent data compactly and control system resources more efficiently and precisely.
It's useful to know if you care about the following questions:
- What is bit value at ith position in a byte? How to set it to different value?
- Count the set bits in a number
- How to clear/set bits after a specific position?
- Extract last set bit from a number
Convert Binary to Decimal
Let's say we have pk,pk-1,pk-2,...,p1,p0 representing the bits of a binary number. The decimal value can be calculated as: 2^k x pk + 2^(k-1) x pk-1 + ... + 2^1 x p1 + 2^0 xp0
Unsigned vs Signed Integers
We can represent both unsigned and signed integers with our bits. The first bit(rightmost) is used as the sign bit. If the sign bit is 0, the number is positive; if it is 1, the number is negative.
If a number is unsigned integer, then the range is 0 to 2^n - 1, where n is the number of bits.
If a number is signed integer, then the range is -2^(n-1) to 2^(n-1) - 1, where n is the number of bits.
One may ask, what's the relationship between signed and unsigned integers? and what if we try to store a number that is out of the range of our data type?
For more information, refer to below resources.