Binary Number System

Definition

According to digital electronics and mathematics, a binary number is defined as a number that is expressed in the binary system or base 2 numeral system. It describes numeric values by two separate symbols; 1 (one) and 0 (zero). The base-2 system is the positional notation with 2 as a radix.

The binary system is applied internally by almost all latest computers and computer-based devices because of its direct implementation in electronic circuits using logic gates. Every digit is referred to as a bit. ¹

Single binary digit is a bit. A sequence of four bits (1001) is a nibble and a sequence of eight bits (11001010) is called a byte. Binary represents a specific power of the base (2) of the number system.

Example

Here we will see an example of how to calculate the Decimal Equivalent of a binary number.
Binary Number: 11001₂

11001₂can be written as 11001
Step 1: (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)
Step 2: (16 + 8 + 0 + 0 + 1)₁₀
Step 3: (25)₁₀ or 25

“Bi” in Binary means “two”. Hence, this draws back the line to the representation of a number in terms of 0 and 1 only. It is possible to express decimal numbers in terms of a binary number system easily. Decimal numbers and binary numbers have different notations. A decimal number is represented with a base of 10 while a binary number is represented with a base of 2. For example, 2 in decimal notation is represented as (2)10(2)10. The binary number for 2 is represented as (10)2(10)2. Hence, 10 is the binary number representation for the number 2. ²

References

¹ “Binary Number System – Definition, Conversion And Examples”. 2022. BYJUS. https://byjus.com/maths/binary-number-system/.

² “Binary Number System – Chart, Conversion And Operations”. 2022. CUEMATH. https://www.cuemath.com/numbers/binary-number-system/.

Additional Reading

“Binary Number System – Definition, Conversion, Examples – GeeksForGeeks”. 2022. GeeksForGeeks. https://www.geeksforgeeks.org/binary-number-system-definition-conversion-examples/.

Eren, Ilknur. “Binary Number System”. 2018. Medium. https://ilknureren.medium.com/binary-number-system-c1015a413b75.

Videos

Binary numbers – FAST and SIMPLE!

Representing Numbers and Letters with Binary: Crash Course Computer Science #4

The binary number system

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.