ConvertNumber conversionBinary to Decimal Converter

Binary to Decimal Converter

What is Binary to Decimal Conversion?

Binary to decimal conversion is the process of converting a binary number (a number expressed in the base-2 numeral system) into a decimal number (a number expressed in the base-10 numeral system). The binary system uses only two digits, 0 and 1, while the decimal system uses ten digits, from 0 to 9. Understanding how to convert binary to decimal is essential for working with binary data and calculations.

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    Binary Number System

    Binary is a base-2 numeral system used in mathematics and computer science. It uses only two symbols, 0 and 1, to represent numbers. Each digit in a binary number represents a power of 2. For example, the binary number “1010” represents (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 8 + 0 + 2 + 0 = 10 in decimal.

    In computing, binary is fundamental as computers use binary digits (bits) to process and store information. It forms the basis for digital communication, data representation, and computer programming.

    Decimal Number System

    Decimal is the base-10 numeral system, the most commonly used system in everyday life. It uses ten symbols (0 to 9) to represent numbers. Each digit in a decimal number represents a power of 10. For example, the decimal number “325” represents (3 * 10^2) + (2 * 10^1) + (5 * 10^0) = 300 + 20 + 5 = 325.

    Binary to Decimal

    How to Convert Binary to Decimal

    Steps for Binary to Decimal Conversion:

    1. Write down the binary number.
    2. List the powers of 2 from right to left, starting with 20.
    3. Multiply each binary digit by the corresponding power of 2.
    4. Sum all the products.

    Example:

    Convert the binary number 11012 to decimal:

    Write down the binary number: 11012

    List the powers of 2 from right to left:

    23, 22, 21, 20

    Multiply each binary digit by the corresponding power of 2:

    1 × 23 = 1 × 8 = 8

    1 × 22 = 1 × 4 = 4

    1 × 21 = 1 × 2 = 0

    1 × 20 = 1 × 1 = 1

    Sum all the products:

    8 + 4 + 0 + 1 = 13

    Therefore, the binary number 11012 is equal to the decimal number 1310

    Binary to Decimal Conversion Table

    Here is a table containing some binary to decimal converted numbers:

    Binary
    Number
    Decimal
    Number
    Hex
    Number
    0 0 0
    1 1 1
    10 2 2
    11 3 3
    100 4 4
    101 5 5
    110 6 6
    111 7 7
    1000 8 8
    1001 9 9
    1010 10 A
    1011 11 B
    1100 12 C
    1101 13 D
    1110 14 E
    1111 15 F
    10000 16 10
    10001 17 11
    10010 18 12
    10011 19 13
    10100 20 14
    10101 21 15
    10110 22 16
    10111 23 17
    11000 24 18
    11001 25 19
    11010 26 1A
    11011 27 1B
    11100 28 1C
    11101 29 1D
    11110 30 1E
    11111 31 1F
    100000 32 20
    1000000 64 40
    10000000 128 80
    100000000 256 100

    Binary to Decimal Formula

    Here is the Binary to Decimal formula:

    Binary to Decimal Formula

    FAQs on Binary to Decimal Converter

    How to convert binary to decimal?

    Converting binary to decimal involves multiplying each binary digit by its corresponding power of 2 and then adding up the results. Start from the rightmost digit and move to the left, with the rightmost digit corresponding to 2^0 (1) and each subsequent digit doubling in value (2^1, 2^2, 2^3, and so on).

    How do you convert 10101 binary to decimal?

    To convert 10101 binary to decimal: 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 = 16 + 0 + 4 + 0 + 1 = 21 (decimal)

    How do you turn 1011 into a decimal?

    To convert 1011 binary to decimal: 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 0 + 2 + 1 = 11 (decimal)

    How to convert binary to decimal 111010?

    To convert 111010 binary to decimal: 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 32 + 16 + 8 + 0 + 2 + 0 = 58 (decimal)

    What is 1111 in decimal?

    To convert 1111 binary to decimal: 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 8 + 4 + 2 + 1 = 15 (decimal)

    How to convert 1100 binary to decimal?

    To convert 1100 binary to decimal: 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 0 * 2^0 = 8 + 4 + 0 + 0 = 12 (decimal)

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