Easy way to convert from Binary number into Decimal number

Convert from binary into decimal is an easy process. Binary, or base 2, is a positional number system with 2 digits, which are 0 and 1. The value of each digit also depends on its position in the number, starting from the rightmost digit, which represents the ones place, followed by the twos place, fours place, eights place, and so on. For example, the binary number 1011 represents 1 * 8 + 0 * 4 + 1 * 2 + 1 * 1, which is equal to 11 in decimal.

Decimal, or base 10, is a positional number system with 10 digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The value of each digit depends on its position in the number, starting from the rightmost digit, which represents the ones place, followed by the tens place, hundreds place, and so on. For example, the decimal number 1234 represents 1 * 1000 + 2 * 100 + 3 * 10 + 4 * 1, which is equal to 1234.

Computers use the binary number system to represent data and perform calculations, while decimal is the number system commonly used in everyday life.

How to convert a binary number to a decimal number

To convert a binary number to a decimal number, follow these steps:

1. Write down the binary number you want to convert. For example, let’s say we want to convert the binary number 1010 to decimal.
2. Write down the place values of each digit in the binary number. The rightmost digit has a place value of 1, the second digit from the right has a place value of 2, the third digit from the right has a place value of 4, the fourth digit from the right has a place value of 8, and so on.
3. Multiply each digit in the binary number by its corresponding place value, and add up the results. For example:

1 * 0 + 2 * 1 + 4 * 0 + 8 * 1 = 10

So the decimal equivalent of the binary number 1010 is 10.

Here’s another example. Let’s say we want to convert the binary number 110110 to decimal:

1. Write down the binary number: 110110
2. Write down the place values of each digit: 1, 2, 4, 8, 16, 32
3. Multiply each digit in the binary number by its corresponding place value, and add up the results:

1 * 0 + 2 * 1 + 4 * 1 + 8 * 0 + 16 * 1 + 32 * 1 = 54

So, the decimal equivalent of the binary number 110110 is 54.

How to convert decimal to binary

To convert a decimal number to a binary number, follow these steps:

1. Divide the decimal number by 2, and write down the quotient and the remainder. For example, let’s say we want to convert the decimal number 14 to binary:

14 ÷ 2 = 7 with a remainder of 0

2. Divide the quotient by 2, and write down the new quotient and remainder. For example:

7 ÷ 2 = 3 with a remainder of 1

3. Continue the process of dividing the quotient by 2 and writing down the new quotient and remainder until the quotient becomes 0. For example:

3 ÷ 2 = 1 with a remainder of 1
1 ÷ 2 = 0 with a remainder of 1

4. Write down the remainders in reverse order. For example:

The remainders are 1, 1, 0, and 0, so the binary equivalent of the decimal number 14 is 1110.

Therefore, the binary equivalent of the decimal number 14 is 1110.

The Equivalent between binary number and decimal number

Here are the decimal and binary equivalents of the numbers 0 to 15:

In the binary system, each digit can only have a value of 0 or 1, and the place value of each digit doubles as you move left. For example, the binary number 1011 represents:

1 * 8 + 0 * 4 + 1 * 2 + 1 * 1 = 11

Conversely, in the decimal system, each digit can have a value of 0 to 9, and the place value of each digit increases by a factor of 10 as you move left. For example, the decimal number 27 can be represented in binary as:

1 * 16 + 1 * 8 + 0 * 4 + 1 * 2 + 1 * 1 = 27

Which formula we used on binary?

There are many different formulas and operations that can be used with binary numbers, just like with decimal numbers. Here are a few common ones:

1. Binary addition: Adding two binary numbers together is similar to decimal addition, except that the numbers are added digit-by-digit, and carrying over to the next digit happens when the sum is greater than 1. For example:

csharpCopy code 1011 (decimal 11)

• 1101 (decimal 131 1000 (decimal24)

2. Binary subtraction: Subtracting one binary number from another is similar to decimal subtraction, except that borrowing from the next digit happens when the digit being subtracted is greater than the digit being subtracted from. For example:

csharpCopy code 1101 (decimal 13)

1011 (decimal 11)10 (decimal 2)

3. Binary multiplication: Multiplying two binary numbers together is similar to decimal multiplication, except that there are only two possible values for each digit (0 or 1), and the partial products are shifted to the left according to their place value. For example:

sqlCopy code 101 (decimal 5) x 110 (decimal 6) ----- 1010 (decimal 10) 101 10010 (decimal 30)

4.. Binary division: Dividing one binary number by another is similar to decimal division, except that it can be more complicated due to the limited number of possible values for each digit. It often involves repeated subtraction and shifting of the divisor.

What is octal number system

Octal number system is a positional numbering system that uses a base of 8. It is a system that is used to represent numbers using 8 digits, namely 0, 1, 2, 3, 4, 5, 6, and 7.

In the octal number system, each digit represents a power of 8, starting from the rightmost digit, which represents 8^0 or 1, and continuing to the left, with each digit representing the next power of 8. For example, the octal number 247 can be interpreted as:

2 x 8^2 + 4 x 8^1 + 7 x 8^0 = 128 + 32 + 7 = 167

In contrast to decimal numbers that use 10 digits (0-9), octal numbers only use 8 digits (0-7), and the position of the digit within the number determines its value.

The octal number system is commonly used in computer programming, particularly in the representation of machine language instructions and memory addresses, as it is easy to convert to and from binary, which is the native language of computers.

Convert from decimal to octal

To convert a decimal number to its octal equivalent, you can use the following steps:

1. Divide the decimal number by 8.
2. Write down the remainder (in octal) as the rightmost digit of the octal number.
3. Divide the quotient from the previous step by 8.
4. Write down the remainder as the next digit to the left in the octal number.
5. Repeat steps 3 and 4 until the quotient is 0.

Here’s an example of how to convert the decimal number 123 to octal:

1. 123 divided by 8 is 15 with a remainder of 3. So, the rightmost digit in the octal number is 3.
2. Divide 15 by 8. The quotient is 1 with a remainder of 7. So, the next digit to the left in the octal number is 7.
3. Divide 1 by 8. The quotient is 0 with a remainder of 1. So, the next digit to the left in the octal number is 1.
4. The quotient is now 0, so we stop.

Therefore, the octal equivalent of decimal number 123 is 173.

Convert binary to octal

To convert a binary number to its octal equivalent, you can group the binary digits into sets of three starting from the rightmost digit, and then convert each set of three binary digits to its octal equivalent. If the leftmost group has less than three digits, add zeros to the left until the group has three digits. Here are the steps:

1. Group the binary digits into sets of three starting from the rightmost digit.
2. Add zeros to the left of the leftmost group if necessary to make it a complete group of three binary digits.
3. Convert each group of three binary digits to its octal equivalent.
4. Write down the octal digits from each group as a single number, starting from the left.

Here’s an example of how to convert the binary number 11010110 to octal:

1. Group the binary digits into sets of three: 011 010 110
2. Add a zero to the leftmost group to make it a complete group of three binary digits: 011 010 110
3. Convert each group of three binary digits to its octal equivalent: 3 2 6
4. Write down the octal digits from each group as a single number, starting from the left: 326

Therefore, the octal equivalent of the binary number 11010110 is 326.

Convert octal to binary

To convert an octal number to its binary equivalent, you can convert each octal digit to its 3-bit binary equivalent, and then concatenate the resulting binary digits. Here are the steps:

1. Convert each octal digit to its 3-bit binary equivalent.
2. Write down the resulting binary digits as a single number, starting from the left.

Here’s an example of how to convert the octal number 73 to binary:

1. Convert the first octal digit, 7, to its 3-bit binary equivalent: 111
2. Convert the second octal digit, 3, to its 3-bit binary equivalent: 011
3. Write down the resulting binary digits as a single number, starting from the left: 111011

Therefore, the binary equivalent of the octal number 73 is 111011.

Convert octal to decimal

To convert an octal number to its decimal equivalent, you can use the positional notation of the number system. Each digit in an octal number represents a power of 8, starting from 8^0, and increasing by a power of 8 for each position to the left. To convert the octal number to decimal, you can multiply each digit by its corresponding power of 8 and add the results together. Here are the steps:

1. Write down the octal number.
2. Starting from the rightmost digit, assign each digit a positional value based on its position in the number. The rightmost digit has a positional value of 8^0 = 1, the next digit to the left has a positional value of 8^1 = 8, the next digit to the left has a positional value of 8^2 = 64, and so on, increasing by a power of 8 for each position to the left.
3. Multiply each digit by its positional value.
4. Add the results of the multiplication together.

Here’s an example of how to convert the octal number 625 to decimal:

1. Write down the octal number: 625
2. Assign each digit a positional value: 5 has a positional value of 8^0 = 1, 2 has a positional value of 8^1 = 8, and 6 has a positional value of 8^2 = 64.
3. Multiply each digit by its positional value: 5 x 1 = 5, 2 x 8 = 16, and 6 x 64 = 384.
4. Add the results of the multiplication together: 5 + 16 + 384 = 405.

Therefore, the decimal equivalent of the octal number 625 is 405.

What is hexadecimal number system

The hexadecimal number system is a base-16 number system that uses 16 unique symbols to represent numbers. The symbols used are the 10 decimal digits (0-9) and six additional symbols, usually the letters A through F, to represent values 10 to 15.

Similar to the decimal system, each position in a hexadecimal number represents a power of 16, starting with 16^0 in the rightmost position and increasing by a power of 16 for each position to the left. For example, the hexadecimal number 3F can be expanded as:

csharpCopy code3F = 3 × 16^1 + 15 × 16^0
   = 48 + 15
   = 63 (in decimal)

Hexadecimal numbers are commonly used in computer science and digital electronics because they can represent large values using relatively few digits. For example, a byte of data (8 bits) can be represented by two hexadecimal digits, while it would require three decimal digits. Hexadecimal is also used in color representation, where each color is represented by a combination of red, green, and blue components, each of which can take values from 0 to 255, or 00 to FF in hexadecimal.

Convert binary to hexadecimal

To convert a binary number to its hexadecimal equivalent, you can group the binary digits into sets of four starting from the rightmost digit, and then convert each set of four binary digits to its hexadecimal equivalent. If the leftmost group has less than four digits, add zeros to the left until the group has four digits. Here are the steps:

1. Group the binary digits into sets of four starting from the rightmost digit.
2. Add zeros to the left of the leftmost group if necessary to make it a complete group of four binary digits.
3. Convert each group of four binary digits to its hexadecimal equivalent.
4. Write down the hexadecimal digits from each group as a single number, starting from the left.

Here’s an example of how to convert the binary number 11010110 to hexadecimal:

1. Group the binary digits into sets of four: 1101 0110
2. Add a zero to the leftmost group to make it a complete group of four binary digits: 1101 0110
3. Convert each group of four binary digits to its hexadecimal equivalent: D 6
4. Write down the hexadecimal digits from each group as a single number, starting from the left: D6

Therefore, the hexadecimal equivalent of the binary number 11010110 is D6.

Convert decimal to hexadecimal

To convert a decimal number to its hexadecimal equivalent, you can use the remainder method. In this method, you repeatedly divide the decimal number by 16 and write down the remainder for each division in hexadecimal format. The remainders are then read in reverse order to get the hexadecimal equivalent. Here are the steps:

1. Write down the decimal number.
2. Divide the decimal number by 16 and write down the quotient and remainder.
3. Divide the quotient from step 2 by 16 and write down the new quotient and remainder.
4. Repeat step 3 until the quotient is 0.
5. Write down the remainders from each division in reverse order, using the hexadecimal digits 0-9 and A-F to represent values 0-15.

Here’s an example of how to convert the decimal number 347 to hexadecimal:

1. Write down the decimal number: 347
2. Divide 347 by 16: 347 ÷ 16 = 21 remainder 11. Write down the remainder in hexadecimal format as B.
3. Divide 21 by 16: 21 ÷ 16 = 1 remainder 5. Write down the remainder in hexadecimal format as 5.
4. Divide 1 by 16: 1 ÷ 16 = 0 remainder 1. Write down the remainder in hexadecimal format as 1.
5. Write down the remainders from each division in reverse order: 151B.

Therefore, the hexadecimal equivalent of the decimal number 347 is 151B.

Convert octal to hexadecimal

To convert an octal number to its hexadecimal equivalent, you can first convert the octal number to binary and then convert the binary number to hexadecimal. Here are the steps:

1. Write down the octal number.
2. Replace each octal digit with its binary equivalent using a table or by converting each digit to a 3-bit binary number.
3. Group the binary digits into sets of four starting from the rightmost digit. Add zeros to the leftmost group if necessary to make it a complete group of four binary digits.
4. Convert each group of four binary digits to its hexadecimal equivalent using a table or by converting each group to its decimal equivalent and then to its hexadecimal equivalent.
5. Write down the hexadecimal digits from each group as a single number, starting from the left.

Here’s an example of how to convert the octal number 723 to hexadecimal:

1. Write down the octal number: 723
2. Convert each octal digit to its binary equivalent: 7 = 111, 2 = 010, 3 = 011
3. Group the binary digits into sets of four: 0111 0100 0011
4. Convert each group of four binary digits to its hexadecimal equivalent: 7 4 3
5. Write down the hexadecimal digits from each group as a single number, starting from the left: 743

Therefore, the hexadecimal equivalent of the octal number 723 is 743.

Convert from hexadecimal to binary

To convert a hexadecimal number to its binary equivalent, you can convert each hexadecimal digit to its 4-bit binary equivalent. Here are the steps:

1. Write down the hexadecimal number.
2. Convert each hexadecimal digit to its 4-bit binary equivalent using a table or by converting each digit to its decimal equivalent and then to its binary equivalent.
3. Write down the 4-bit binary equivalents of each hexadecimal digit as a single number, starting from the left.

Here’s an example of how to convert the hexadecimal number 3A7F to binary:

1. Write down the hexadecimal number: 3A7F
2. Convert each hexadecimal digit to its 4-bit binary equivalent: 3 = 0011, A = 1010, 7 = 0111, F = 1111
3. Write down the 4-bit binary equivalents of each hexadecimal digit as a single number, starting from the left: 0011101011111111

Therefore, the binary equivalent of the hexadecimal number 3A7F is 0011101011111111.

Convert hexadecimal to decimal

To convert a hexadecimal number to its decimal equivalent, you can use the position value method. In this method, you multiply each hexadecimal digit by its position value and then add up the results. Here are the steps:

1. Write down the hexadecimal number.
2. Assign a position value to each digit, starting from the rightmost digit and increasing by a power of 16 for each position.
3. Convert each hexadecimal digit to its decimal equivalent using a table or by converting each digit to its binary equivalent and then to its decimal equivalent.
4. Multiply each digit by its position value.
5. Add up the results from step 4.

Here’s an example of how to convert the hexadecimal number 3A7F to decimal:

1. Write down the hexadecimal number: 3A7F
2. Assign a position value to each digit: F (position 0), 7 (position 1), A (position 2), 3 (position 3)
3. Convert each hexadecimal digit to its decimal equivalent: F = 15, 7 = 7, A = 10, 3 = 3
4. Multiply each digit by its position value: 15 x 16^0 + 7 x 16^1 + 10 x 16^2 + 3 x 16^3
5. Add up the results from step 4: 15 + 112 + 2560 + 12288 = 14975

Therefore, the decimal equivalent of the hexadecimal number 3A7F is 14975.

10 example of binary, decimal, octal and hexadecimal conversion

Here are 10 examples of binary, decimal, octal, and hexadecimal conversions:

1. Binary to Decimal: 10101 (binary) = 21 (decimal) Decimal to Octal: 21 (decimal) = 25 (octal) Octal to Hexadecimal: 25 (octal) = 0x15 (hexadecimal)
2. Decimal to Binary: 93 (decimal) = 01011101 (binary) Binary to Octal: 01011101 (binary) = 135 (octal) Octal to Hexadecimal: 135 (octal) = 0x5D (hexadecimal)
3. Octal to Binary: 647 (octal) = 110100111 (binary) Binary to Decimal: 110100111 (binary) = 423 (decimal) Decimal to Hexadecimal: 423 (decimal) = 0x1A7 (hexadecimal)
4. Hexadecimal to Binary: 0x9B (hexadecimal) = 10011011 (binary) Binary to Decimal: 10011011 (binary) = 155 (decimal) Decimal to Octal: 155 (decimal) = 233 (octal)
5. Decimal to Binary: 177 (decimal) = 10110001 (binary) Binary to Octal: 10110001 (binary) = 261 (octal) Octal to Hexadecimal: 261 (octal) = 0xB1 (hexadecimal)
6. Octal to Decimal: 633 (octal) = 411 (decimal) Decimal to Binary: 411 (decimal) = 110011011 (binary) Binary to Hexadecimal: 110011011 (binary) = 0x1CB (hexadecimal)
7. Hexadecimal to Binary: 0x3E8 (hexadecimal) = 1111101000 (binary) Binary to Decimal: 1111101000 (binary) = 1000 (decimal) Decimal to Octal: 1000 (decimal) = 1750 (octal)
8. Binary to Decimal: 11001110 (binary) = 206 (decimal) Decimal to Octal: 206 (decimal) = 316 (octal) Octal to Hexadecimal: 316 (octal) = 0xCE (hexadecimal)
9. Decimal to Binary: 78 (decimal) = 1001110 (binary) Binary to Octal: 1001110 (binary) = 116 (octal) Octal to Hexadecimal: 116 (octal) = 0x4E (hexadecimal)
10. Octal to Binary: 775 (octal) = 111111101 (binary) Binary to Decimal: 111111101 (binary) = 509 (decimal) Decimal to Hexadecimal: 509 (decimal) = 0x1FD (hexadecimal)

1. Binary to Decimal Conversion:

To convert a binary number to its decimal equivalent, we use the positional value method. We start from the rightmost digit, which has a position value of 2^0, and then we double the position value for each digit to the left. To convert a binary digit to its decimal equivalent, we simply multiply the digit by its position value. Then we add up the results for each digit to get the decimal equivalent.

For example, to convert the binary number 10101 to decimal, we start from the rightmost digit, which is 1. Its position value is 2^0 = 1. So we multiply 1 by 1, which gives us 1. The next digit to the left is also 1, with a position value of 2^1 = 2. So we multiply 1 by 2, which gives us 2. The third digit to the left is 0, so we don’t need to add anything to the sum. The fourth digit to the left is also 1, with a position value of 2^3 = 8. So we multiply 1 by 8, which gives us 8. The fifth and leftmost digit is also 0, so we don’t need to add anything to the sum. Adding up the results, we get 1 + 2 + 0 + 8 + 0 = 21. Therefore, the decimal equivalent of the binary number 10101 is 21.

2. Decimal to Octal Conversion:

To convert a decimal number to its octal equivalent, we use the positional value method again. We start from the rightmost digit, which has a position value of 8^0 = 1, and then we multiply the position value by 8 for each digit to the left. To convert a decimal digit to its octal equivalent, we repeatedly divide the digit by 8 and then take the remainder. We write down the remainders from right to left to get the octal equivalent.

For example, to convert the decimal number 21 to octal, we start from the rightmost digit, which is 1. Its position value is 8^0 = 1. So we divide 1 by 8, which gives us a quotient of 0 and a remainder of 1. The next digit to the left is 2, with a position value of 8^1 = 8. So we divide 2 by 8, which gives us a quotient of 0 and a remainder of 2. The octal equivalent of the number 21 is 21 (octal), which we get by writing down the remainders from right to left. Therefore, the octal equivalent of the decimal number 21 is 25.

3. Octal to Hexadecimal Conversion:

To convert an octal number to its hexadecimal equivalent, we can use a direct conversion table that maps each octal digit to its hexadecimal equivalent.

For example, to convert the octal number 25 to hexadecimal, we first write down the conversion table:

Then we replace each octal digit with its hexadecimal equivalent to get the hexadecimal equivalent of the whole number. In this case, the octal number 25 corresponds to the hexadecimal number 0.

The octal number 25 corresponds to the hexadecimal number 0x15. Therefore, the hexadecimal equivalent of the octal number 25 is 0x15.

4. Hexadecimal to Binary Conversion:

To convert a hexadecimal number to its binary equivalent, we can use a direct conversion table that maps each hexadecimal digit to its binary equivalent.

For example, to convert the hexadecimal number 0x15 to binary, we first write down the conversion table:

Then we replace each hexadecimal digit with its binary equivalent to get the binary equivalent of the whole number. In this case, the hexadecimal number 0x15 corresponds to the binary number 00010101. Therefore, the binary equivalent of the hexadecimal number 0x15 is 00010101.

5. Decimal to Hexadecimal Conversion:

To convert a decimal number to its hexadecimal equivalent, we can use the same positional value method as in the decimal to octal conversion. We start from the rightmost digit, which has a position value of 16^0 = 1, and then we multiply the position value by 16 for each digit to the left. To convert a decimal digit to its hexadecimal equivalent, we repeatedly divide the digit by 16 and then take the remainder. If the remainder is greater than 9, we replace it with the corresponding letter (A for 10, B for 11, and so on). We write down the remainders from right to left to get the hexadecimal equivalent.

For example, to convert the decimal number 305 to hexadecimal, we start from the rightmost digit, which is 5. Its position value is 16^0 = 1. So we divide 5 by 16, which gives us a quotient of 0 and a remainder of 5. The next digit to the left is 0, so we don’t need to add anything to the sum. The third digit to the left is 3, with a position value of 16^2 = 256. So we divide 3 by 16, which gives us a quotient of 0 and a remainder of 3. The hexadecimal equivalent of the number 305 is 0x131 (or simply 131), which we get by writing down the remainders from right to left and replacing the remainders greater than 9 with the corresponding letters. Therefore, the hexadecimal equivalent of the decimal number 305 is 0x131.

6. Octal to Decimal Conversion:

To convert an octal number to its decimal equivalent, we use the same positional value method as in the binary to decimal conversion. We start from the rightmost digit, which has a position value of 8^0 = 1, and then we multiply the position value by 8 for each digit to the left. To convert an octal digit to its decimal equivalent, we simply multiply the digit by its position value. Then we add up the results for each digit to get the decimal equivalent.

For example

, to convert the octal number 37 to decimal, we start from the rightmost digit, which is 7. Its position value is 8^0 = 1. So we multiply 7 by 1, which gives us 7. The next digit to the left is 3, with a position value of 8^1 = 8. So we multiply 3 by 8, which gives us 24. The decimal equivalent of the number 37 is 31, which we get by adding up the results for each digit. Therefore, the decimal equivalent of the octal number 37 is 31.

7. Octal to Binary Conversion:

To convert an octal number to its binary equivalent, we can first convert each octal digit to its 3-bit binary equivalent using a conversion table.

Then we simply concatenate the 3-bit binary equivalents of each octal digit to get the binary equivalent of the whole number.

For example, to convert the octal number 37 to binary, we first convert each octal digit to its 3-bit binary equivalent: 3 -> 011 and 7 -> 111. Then we concatenate these 3-bit binary equivalents to get the binary number 011111. Therefore, the binary equivalent of the octal number 37 is 011111.

8. Hexadecimal to Decimal Conversion:

To convert a hexadecimal number to its decimal equivalent, we use the same positional value method as in the octal to decimal conversion. We start from the rightmost digit, which has a position value of 16^0 = 1, and then we multiply the position value by 16 for each digit to the left. To convert a hexadecimal digit to its decimal equivalent, we multiply the digit by its position value. If the digit is a letter (A-F), we replace it with its corresponding decimal value (A=10, B=11, and so on). Then we add up the results for each digit to get the decimal equivalent.

For example, to convert the hexadecimal number 0x1A to decimal, we start from the rightmost digit, which is A. Its position value is 16^0 = 1. So we multiply 10 (the decimal equivalent of A) by 1, which gives us 10. The next digit to the left is 1, with a position value of 16^1 = 16. So we multiply 1 by 16, which gives us 16. The decimal equivalent of the number 0x1A is 26, which we get by adding up the results for each digit. Therefore, the decimal equivalent of the hexadecimal number 0x1A is 26.

9. Hexadecimal to Octal Conversion:

To convert a hexadecimal number to its octal equivalent, we can first convert the hexadecimal number to its binary equivalent using the method described earlier. Then we group the binary digits into groups of 3, starting from the rightmost digit, and convert each group of 3 binary digits to its octal equivalent using the conversion table described earlier.

For example, to convert the hexadecimal number 0x1A to octal, we first convert it to binary: 0x1A -> 00011010. Then we group the binary digits into groups of 3, starting from the rightmost digit: 000 110 10. Finally, we convert each group of 3 binary digits to its octal equivalent using the conversion table: 000 -> 0, 110 -> 6, and 10 -> 2. So the octal equivalent of the hexadecimal number 0x1A is 062.