Introduction to bitshift operations

Introduction

Bitshift is the action of shift a bit from one position to another in order to multiply or divide a binary number. For example, if I want to perform a multiplication on number 0001 I’ll shift it one bit to the left, and the result will be 0010. To understand it better, let’s remember how we are used to multiply numbers.

Base 10

We are used to perform mathematical operations on top of the Base 10, which has the following ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. When we want to multiply one number to another, the result will be composed by one or more of those ten numbers (e.g. 5 * 7 = 35). Multiplying or dividing numbers by 10 will give you interesting results:

• 10 * 10 = 100;
• 509 * 10 = 5090;
• 1000 / 10 = 100;

Let’s vizualize it in another way, filling the “blank” spaces with zero:

• 0010 * 10 = 0100;
• 0509 * 10 = 5090;
• 1000 / 10 = 0100;

As you can see, multiplying or dividing a Base 10 number by 10 is the same as shifting this number to the left (multiplication) or to the right (division). You can do something similar with binary numbers.

Base 2

While on Base 10 we can operate with 10 numbers, as you can conclude, the Base 2 let us operate only with 2 numbers: 0, 1. When you think about electronic devices such as a computer this Base is very useful, because it can represent an electrical sign set as ON or OFF (turning a bit on or off - 0 or 1 - respectively).

Performing mathematical operations over Base 2 numbers follows the same logic as with Base 10 numbers, but with Base 10 we have a richier representation. For example, 0001 + 0001 = 0010 (which is 2 on Base 10), because since we only have two numbers, we need more space (more bits) to represent the whole result.

Each bit can contain only 0 or 1, so we can conclude that the maximum number that the first bit can hold is 2ˆ0 (which, of course, is 1), the second bit can hold 2ˆ1 + 2^0 = 3, the third bit can hold 2^2 + 2^1 + 2^0 = 7, and so on. So, every time we add more bits we can hold more numbers. For example, the maximum number a binary with four bits can hold is 2^3 + 2^2 + 2^1 + 2^0 = 15, so 1111 = 15:

1		1		1		1
2^3	+	2^2	+	2^1	+	2^0

Bitshifting

As multiplying or dividing a Base 10 number by 10 the result is a number shifted to the left or to the right, if we multiply or divide a Base 2 number by 2^N (two to the power of number N) the result will be a bit shifted to the left or to the right as well. The syntax that most programming language uses to represent this operation is:

• Bitshift left (multiplication): <<;
• Bitshift right (division): >>;

Examples:

• 0001 << 2^1 = 0010, because 1 * 2 = 2;
• 0100 >> 2^1 = 0010, because 4 / 2 = 2;
• 1000 >> 2^2 = 0010, because 8 / 4 = 2;

The bitshift operations are usefull especially if you are programming an old processor, which don’t have the multiplication or division operation on it, so you can avoid do a bunch of additions or subtractions in order to achieve a result. But, for most cases you won’t need it.

If you want to learn more about it, take a look at this course, the author also explain signed and unsigned operations.

Thanks for reading this post! Bye 👋🏾