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.

⭐ McBride, Martin. 2023. “History and Application of Binary Numbers.” Medium. Graphic maths. September 1. https://medium.com/recreational-maths/history-and-application-of-binary-numbers-f8b582ffe4da.

We tend to think of binary numbers as being a modern concept developed as part of computer science. But in fact, some elements of the binary system were known in ancient times, because they were very useful in many fields back then. This article explains how binary numbers work, but it will also cover some of the history, as it is useful to know where the ideas of binary numbers came from.

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

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