Binary is a number system that uses only two digits, 0 and 1. In computing, binary is the most fundamental way of representing data and instructions, as computers operate on binary signals.
In binary, each digit is called a bit (short for binary digit). A sequence of 8 bits is called a byte, and a sequence of 4 bits is called a nibble. Binary numbers are read from right to left, with the rightmost bit representing the least significant bit (LSB) and the leftmost bit representing the most significant bit (MSB).
Here is an example of how to convert a decimal number to binary:
Let's convert the decimal number 13 to binary.
Divide the decimal number by 2, and write down the remainder. 13 ÷ 2 = 6 with a remainder of 1
Divide the quotient by 2, and write down the remainder. 6 ÷ 2 = 3 with a remainder of 0
Repeat step 2 until the quotient is 0. 3 ÷ 2 = 1 with a remainder of 1 1 ÷ 2 = 0 with a remainder of 1
The binary number is the sequence of remainders, read from bottom to top. 13 in binary is 1101.
Therefore, the binary representation of the decimal number 13 is 1101.
In binary, each bit can be either 0 or 1, and the value of the number is determined by the position of the bits. For example, the binary number 1101 represents:
1 x 2^3 + 1 x 2^2 + 0 x 2^1 + 1 x 2^0 = 8 + 4 + 0 + 1 = 13
So, in binary, the same number is represented with fewer digits than in decimal.
