Binary Digits Meaning
The binary digit, also known as the bit is a basic unit of information in computer and digital communication. A single binary digit is known as a bit. The binary digits represent logical code with one more two possible values. These two possible values are represented as either 0 or 1.
In Mathematics, binary numbers are made up of binary digits. In other words, binary numbers require only 2 digits to represent any number instead of 10 different symbols that are used in the decimal number system. Hence, the decimal numbers from 1 to 10 in binary are represented as
Also, binary numbers can be easily converted into other number systems like decimal number systems, hexadecimal number systems, octal number systems, and vice versa. Here, we will discuss binary number to decimal number conversion, and decimal number to binary number with a decimal point.
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Binary Number to Decimal Number Conversion
To convert binary numbers to decimal numbers, we use the multiplication method. In this method, if a base 2 has to be converted into base 10, then each digit of a given number is multiplied from the most significant digit to the least significant digit with reducing the power of the base. Following are the steps to convert binary numbers to decimal numbers.
Step 1: Write down the binary number and calculate the place value of each digit.
Step 2: Starting from the most significant digit to the least significant digit, multiply each digit of the given binary number by the corresponding power of 2.
Step 3: Add up the results obtained to convert the given binary number into the decimal number.
Let us understand with an example:
Convert the Binary Number 1110₂ into a Decimal Number.
Step 1: Calculate the place values
As 1110 has four digits, so we have four place values: 2º, 2¹, 2², and 2³
Step 2: Multiply each digit by the corresponding power 2
1 x 2³ = 8 1 x 2² = 4 1 x 2¹ = 2 0 x 2º = 0
Step 3: Sum up the result to get the given binary number into decimal numbers.
= 8 + 4+ 2 + 0
= 14
Decimal Number To Binary Number Conversion
Let us now understand how to convert decimal number to binary number through the following steps:
Divide the given decimal number by 2. By dividing the number by 2, the result will be obtained along with the remainder.
If the given decimal number is even, the result obtained will be the whole number, and the remainder will be 0.
If the given decimal number is odd, the result obtained will not be completely divided and will give the remainder 0.
The binary number will be obtained by placing all the remainders in order in such a way, the Least Significant Bit at the top and the Most Significant Bit at the bottom
Let us understand with an example:
Convert 294₁₀ into a Binary Number
Hence, 294.46₁₀ is 100100110₂
Decimal to Binary with Decimal Point Conversion
To convert decimal numbers to binary with a decimal point, we convert both integer and fractional parts individually and then add the values to get equivalent binary numbers. Let us understand with an example:
Convert 294.46₁₀ To Binary
To convert 98.46₁₀ to binary, we first convert the integer part that is 98 and then fractional parts that is 46. Further, we will add the values of both parts to get equivalent binary numbers.
Following are the steps to convert integer 294 to decimal:
Divide 294 by 2 and keep observing both quotient and remainder value. Continue dividing the quotient by 2 till you get the quotient value 0.
As 295 is an even number, the result will be the whole number and it gives the remainder 0.
Then just write the remainder value in reverse order to get an equivalent binary number.
Hence, 294.46₁₀ is 100100110₂
Following are the steps to convert decimal fraction 0.46 to decimal number
Step 1: Multiply the decimal fraction 0.46 by 2 and keep observing both integer and fractional values. Continue multiplying the decimal fraction by 2, till you get the resultant fractional values equal to 0.
Step 2: In this step, write down the integer part from the result of each multiplication to get an equivalent binary number.
Hence, the decimal number 0.46 in binary is 0.0111010111₂.
Therefore, the decimal number 292.46 in binary is 100100110. 0111010111₂.
Solved Examples
1. Convert the Binary Number 1011₂ in Decimal Number.
Step 1: Calculate the place values
As 1011 has four digits, so we have four place values: 2º, 2¹, 2², and 2³
Step 2: Multiply each digit by the corresponding power 2
1 x 2³ = 8 0 x 2² = 0 1 x 2¹ = 2 1x 2º = 1
Step 3: Sum up the result to get the given binary number into decimal numbers.
= 8 + 0+ 2 + 0
= 11
Hence, 1011₂ is 14₁₀
2. Convert the Decimal Number 16 into a Binary Number
Hence, 16₁₀ is 10000₂
FAQs on Binary Digits
Q1. What is Bit (Binary Digit)?
Ans. A bit (binary digit) is the smallest unit of data in a computer. The binary digits are used for storing information and have a value of true/false, or on/off. A single binary digit is known as a bit. A single bit has a value of either 0 or 1, which is often used to store information or data and execute instructions in multiple bits known as bytes.
Q2. What are Decimal Number Systems in Mathematics?
Ans. In Mathematics, decimal number systems, also known as positional number systems, employ 10 as a base and require 10 different digits such as 0,1,2,3,4,5,6,7,8, and 9 to represent the number. It also required a decimal point to represent the fraction. In these stems, the numerals used to represent the numbers take different place values depending upon the position. For example, in a base 10 system the number 543.21 represents the sum ( 5 x 10²) + ( 4 x 10¹) + ( 3 x 10º) + ( 2 ÷ 10⁻¹) + (1 x 10)⁻².
Q3. What is the Use of Binary Numbers in Computers?
Ans. Binary numbers are commonly used in computer applications. Computers use binary digits 0 and 1 to store information. A bit or binary digit is the smallest unit of data in computing. It is represented by a 0 or a 1.
Everything on computers is represented in the form of binary systems. Images, audios, and characters all look like binary numbers in machine code. These numbers are encoded in different data to give them meaning. For example, 8-bit pattern 01000001 could be number 65, character A, or colour in an image.
