What Are Binary Digits and How to Convert Using Base 2
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 in the Base 2 Number System
1. What are binary digits?
Binary digits are the two symbols 0 and 1 used in the binary number system to represent numbers. In base-2, every number is written using only these two digits. Each binary digit is called a bit, and combinations of bits are used in mathematics and computer systems to represent values and data.
2. What is the binary number system?
The binary number system is a base-2 number system that uses only the digits 0 and 1. Unlike the decimal system (base-10), which uses powers of 10, binary numbers use powers of 2. For example:
- Decimal place values: 1, 10, 100, 1000
- Binary place values: 1, 2, 4, 8, 16 (powers of 2)
3. How do you convert a binary number to decimal?
To convert a binary number to decimal, multiply each digit by its corresponding power of 2 and add the results. Steps:
- Write place values (powers of 2).
- Multiply each binary digit by its place value.
- Add all the products.
- (1×8) + (0×4) + (1×2) + (1×1)
- = 8 + 0 + 2 + 1
- = 11
4. How do you convert a decimal number to binary?
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. Steps:
- Divide the number by 2.
- Write down the remainder (0 or 1).
- Repeat with the quotient until it becomes 0.
- Read the remainders from bottom to top.
- 10 ÷ 2 = 5 remainder 0
- 5 ÷ 2 = 2 remainder 1
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
5. What does each position in a binary number represent?
Each position in a binary number represents a power of 2. Starting from the rightmost digit:
- 2⁰ = 1
- 2¹ = 2
- 2² = 4
- 2³ = 8
- 2⁴ = 16
6. What is the value of 1 byte in binary digits?
One byte is equal to 8 binary digits (8 bits). A bit is a single binary digit (0 or 1), and 8 bits grouped together form one byte. For example, 10101100 is an 8-bit binary number representing one byte.
7. What is the largest number you can write with 4 binary digits?
The largest number that can be written with 4 binary digits is 1111₂, which equals 15₁₀. Since the maximum value occurs when all digits are 1:
- (1×8) + (1×4) + (1×2) + (1×1)
- = 8 + 4 + 2 + 1
- = 15
8. How do you add binary numbers?
Binary addition follows four simple rules based on base-2 arithmetic:
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (write 0, carry 1)
- 101
- + 011
- = 1000
9. Why are only 0 and 1 used in binary?
Only 0 and 1 are used in binary because it is a base-2 system built on two possible states. In mathematics and digital electronics, these two states can represent off/on, false/true, or low/high voltage. Using two digits simplifies calculations and forms the foundation of computer logic and Boolean algebra.
10. What is the difference between binary and decimal numbers?
The main difference is that binary is a base-2 system using digits 0 and 1, while decimal is a base-10 system using digits 0 to 9. Key differences:
- Binary place values: powers of 2 (1, 2, 4, 8, 16)
- Decimal place values: powers of 10 (1, 10, 100, 1000)
- Example: 10 in decimal equals 1010 in binary
