Hexadecimal to Decimal to Octal to Binary Converter

To convert a hexadecimal number to decimal, first convert “A” to 10, “B” to 11, etc. Then, multiply each digit by its corresponding power of 16 and sum the results. Next, convert the decimal number to octal by repeatedly dividing by 8 and noting the remainders. Finally, convert the octal number to binary by representing each octal digit with its 3-bit binary equivalent.

FAQs

How do you convert hexadecimal to binary octal decimal?

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

1. Hexadecimal to Binary: Group each hexadecimal digit (0-F) and convert it to its 4-bit binary equivalent. For example, to convert “3A” to binary:
   • 3 (in hexadecimal) = 0011 (in binary)
   • A (in hexadecimal) = 1010 (in binary) So, “3A” in hexadecimal is “00111010” in binary.
2. Hexadecimal to Octal: First, convert the hexadecimal number to binary and then group the binary digits into sets of 3. Then, convert each group to its octal equivalent. For example, “3A” in hexadecimal is “00111010” in binary, which can be grouped as “001 110 10.” Then, convert each group to octal:
   • 001 (in binary) = 1 (in octal)
   • 110 (in binary) = 6 (in octal)
   • 10 (in binary) = 2 (in octal) So, “3A” in hexadecimal is “162” in octal.
3. Hexadecimal to Decimal: Convert each hexadecimal digit to its decimal equivalent, considering the position value. For example, “3A” in hexadecimal can be calculated as follows:
   • 3 (in hexadecimal) = 3 (in decimal)
   • A (in hexadecimal) = 10 (in decimal, because A represents 10 in hexadecimal) So, “3A” in hexadecimal is 3 * 16 + 10 = 58 in decimal.

What is the octal number for 0110010011001101?

To convert binary to octal, group the binary digits into sets of 3, starting from the right, and then convert each group to its octal equivalent.

For “0110010011001101”:

• 01 100 100 110 011 01
• Convert each group to octal: 01431305 So, the octal representation of “0110010011001101” is “1431305.”

How to convert hex code to binary?

As mentioned earlier, to convert a hexadecimal number to binary, you simply replace each hexadecimal digit with its 4-bit binary equivalent. For example, if you have the hexadecimal code “1E3A,” you can convert it to binary as follows:

• 1 (in hexadecimal) = 0001 (in binary)
• E (in hexadecimal) = 1110 (in binary)
• 3 (in hexadecimal) = 0011 (in binary)
• A (in hexadecimal) = 1010 (in binary)

So, “1E3A” in hexadecimal is “0001111000111010” in binary.

How to convert octal to hexadecimal and hexadecimal to octal?

To convert octal to hexadecimal and vice versa, you can first convert the octal number to binary (or the hexadecimal number to binary), and then from binary to the other base.

1. Octal to Hexadecimal:
   • Convert octal to binary.
   • Convert binary to hexadecimal.
2. Hexadecimal to Octal:
   • Convert hexadecimal to binary.
   • Convert binary to octal.

How to convert hexadecimal to octal?

To convert hexadecimal to octal, follow these steps:

1. Convert hexadecimal to binary.
2. Group the binary digits into sets of 3, starting from the right.
3. Convert each group of binary digits to its octal equivalent.

For example, to convert “1E3A” in hexadecimal to octal:

• 1E3A in hexadecimal = 0001111000111010 in binary
• Group into sets of 3: 000 111 100 011 101 0
• Convert to octal: 034316

So, “1E3A” in hexadecimal is “34316” in octal.

Can we convert hexadecimal to octal?

Yes, you can convert hexadecimal to octal by first converting it to binary and then from binary to octal, as explained above.

How to convert octal to binary?

To convert octal to binary, follow these steps:

1. Convert each octal digit to its 3-bit binary equivalent.
2. Combine the binary representations of the octal digits to form the binary representation of the whole octal number.

For example, to convert octal “567” to binary:

• 5 (in octal) = 101 (in binary)
• 6 (in octal) = 110 (in binary)
• 7 (in octal) = 111 (in binary)

Combine them: “567” in octal is “101110111” in binary.

Why is 786 an octal number?

786 is not an octal number; it is typically a decimal number. In octal notation, valid digits are 0-7. If you see “786” in a different context, it might be a decimal number.

What is 0.6875 as an octal number?

To convert a fraction to octal, you can use a method similar to converting it to binary. Multiply the fraction by 8 repeatedly, noting the integer part of each result. For 0.6875:

0.6875 * 8 = 5.5 0.5 * 8 = 4.0

So, 0.6875 in octal is 0.54.

What is the binary number 10001101010001101111 written in hexadecimal as?

To convert a binary number to hexadecimal, group the binary digits into sets of 4 from right to left, and then convert each group to its hexadecimal equivalent.

For “10001101010001101111”:

• 1000 1101 0100 0110 1111
• Convert each group to hexadecimal: 8D46F

So, the binary number “10001101010001101111” is “8D46F” in hexadecimal.

How do you convert hex to decimal manually?

To convert a hexadecimal number to decimal manually, assign a positional value to each digit in the hexadecimal number, starting from the right and increasing by powers of 16. Then, multiply each digit by its positional value and sum the results.

For example, to convert “1E3A” to decimal:

• A (rightmost digit) = 10 * 16^0 = 10
• 3 (next digit to the left) = 3 * 16^1 = 48
• E = 14 * 16^2 = 3584
• 1 (leftmost digit) = 1 * 16^3 = 4096

Now, add these values together: 10 + 48 + 3584 + 4096 = 7738

So, “1E3A” in hexadecimal is 7738 in decimal.

What is the shortcut to convert hex to binary?

The shortcut to convert a hexadecimal digit to binary is to use a hexadecimal-to-binary conversion table or calculator. Each hexadecimal digit corresponds directly to a 4-bit binary sequence. For example:

• Hex 0 = Binary 0000
• Hex 1 = Binary 0001
• Hex 2 = Binary 0010
• Hex 3 = Binary 0011
• Hex 4 = Binary 0100
• Hex 5 = Binary 0101
• Hex 6 = Binary 0110
• Hex 7 = Binary 0111
• Hex 8 = Binary 1000
• Hex 9 = Binary 1001
• Hex A = Binary 1010
• Hex B = Binary 1011
• Hex C = Binary 1100
• Hex D = Binary 1101
• Hex E = Binary 1110
• Hex F = Binary 1111

So, you can directly substitute each hexadecimal digit with its corresponding 4-bit binary representation.

How to convert octal & hexadecimal to binary and vice versa?

To convert octal and hexadecimal to binary:

• Octal to Binary: Convert each octal digit to its 3-bit binary representation.
• Hexadecimal to Binary: Convert each hexadecimal digit to its 4-bit binary representation.

To convert binary to octal and hexadecimal, group binary digits into sets of 3 (for octal) or 4 (for hexadecimal) from right to left and convert each group to the respective base.

How do I convert octal to hexadecimal without any binary or decimal?

You can directly convert octal to hexadecimal without going through binary or decimal. Each octal digit corresponds directly to a certain number of bits in hexadecimal:

• Octal 0 = Hexadecimal 0
• Octal 1 = Hexadecimal 1
• Octal 2 = Hexadecimal 2
• Octal 3 = Hexadecimal 3
• Octal 4 = Hexadecimal 4
• Octal 5 = Hexadecimal 5
• Octal 6 = Hexadecimal 6
• Octal 7 = Hexadecimal 7

So, for example, if you have the octal number “1234,” you can directly convert it to hexadecimal as “1234” because each octal digit corresponds to the same digit in hexadecimal.

What is 651.124 octal in hexadecimal?

To convert an octal number to hexadecimal, you can first convert it to binary and then from binary to hexadecimal. Here’s how you can do it:

1. Convert octal to binary:
   • 6 (octal) = 110 (binary)
   • 5 (octal) = 101 (binary)
   • 1 (octal) = 001 (binary)
   • 1 (octal) = 001 (binary)
   • 2 (octal) = 010 (binary)
   • 4 (octal) = 100 (binary)

Combine the binary digits: 11010100100100

2. Convert binary to hexadecimal:
   • 1101 = D
   • 0100 = 4

So, 651.124 in octal is equal to D4 in hexadecimal.

What is hexadecimal octal binary?

Hexadecimal (base-16) is a numeral system that uses the digits 0-9 and the letters A-F to represent values. Octal (base-8) is another numeral system that uses the digits 0-7 to represent values. Binary (base-2) is a numeral system that uses only the digits 0 and 1 to represent values. These are different numeral systems with different base values.

How do you convert 1D7F 16 to an octal system number?

To convert a hexadecimal number (1D7F) to octal:

1. Convert hexadecimal to binary:
   • 1 (hex) = 0001 (binary)
   • D (hex) = 1101 (binary)
   • 7 (hex) = 0111 (binary)
   • F (hex) = 1111 (binary)

Combine the binary digits: 0001110101111101

2. Convert binary to octal by grouping into sets of 3 from right to left:
   • 000 111 010 111 110 1

Convert each group to octal:

• 000 = 0
• 111 = 7
• 010 = 2
• 111 = 7
• 110 = 6
• 1 = 1

So, 1D7F (hexadecimal) is equal to 02776 (octal).

Is hexadecimal and octal the same?

No, hexadecimal (base-16) and octal (base-8) are not the same. They are different numeral systems with different base values. Hexadecimal uses the digits 0-9 and the letters A-F to represent values from 0 to 15 in each digit position, while octal uses the digits 0-7 to represent values from 0 to 7 in each digit position.

How to convert hex to octal in C?

In C, you can use standard library functions to convert hexadecimal to octal. Here’s an example:

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#include <stdio.h> int main() { char hexString[] = "1D7F"; // Replace with your hexadecimal value unsigned int hexValue; sscanf(hexString, "%X", &hexValue); printf("Hexadecimal: %s\n", hexString); printf("Octal: %o\n", hexValue); return 0; }

This code reads a hexadecimal string and converts it to an unsigned integer. Then, it prints the value in octal format.

What is the hexadecimal number C6B to octal?

To convert the hexadecimal number C6B to octal:

1. Convert hexadecimal to binary:
   • C (hex) = 1100 (binary)
   • 6 (hex) = 0110 (binary)
   • B (hex) = 1011 (binary)

Combine the binary digits: 110001101011

2. Convert binary to octal by grouping into sets of 3 from right to left:
   • 110 001 101 011

Convert each group to octal:

• 110 = 6
• 001 = 1
• 101 = 5
• 011 = 3

So, C6B (hexadecimal) is equal to 6133 (octal).

How to convert 10010110 binary to octal?

To convert the binary number 10010110 to octal:

1. Group the binary digits into sets of 3 from right to left:
   • 100 101 10
2. Convert each group to octal:
   • 100 = 4
   • 101 = 5
   • 10 = 2

So, 10010110 (binary) is equal to 452 (octal).

How can I convert my number to octal?

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

1. Divide the decimal number by 8 successively to obtain the remainder at each step.
2. Write down the remainders in reverse order to get the octal representation.

For example, to convert the decimal number 123 to octal:

• 123 ÷ 8 = 15 remainder 3
• 15 ÷ 8 = 1 remainder 7
• 1 ÷ 8 = 0 remainder 1

Now, write down the remainders in reverse order: 173

So, the decimal number 123 is equal to 173 in octal.

What is the addition of the binary numbers 11011011010 and 010100101?

To add binary numbers, align them by their positions (similar to decimal addition) and perform addition from right to left. Carry over any overflow to the next column.

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11011011010 + 010100101 -------------- 11100100111

So, the addition of 11011011010 and 010100101 is 11100100111 in binary.

Why 8 in octal is 10?

In octal (base-8) numbering, there are only 8 digits available, which are 0, 1, 2, 3, 4, 5, 6, and 7. When you count beyond 7, you need to use a new digit, just as in decimal (base-10) numbering, you use a new digit when you count beyond 9. In octal, the digit 8 is represented as “10” because it’s one group of 8 with 0 remaining.

What is an illegal octal digit 9 at?

In octal notation, the valid digits are 0 through 7. Therefore, the digit “9” is considered illegal in octal because it exceeds the maximum digit value allowed in this base. Any digit in a number that is larger than 7 in octal is not valid.

Why 9 is not allowed in octal number?

Octal is a base-8 numeral system, which means it uses only 8 distinct digits (0-7). This limitation arises from the nature of octal as a positional numeral system. Each digit’s value is determined by its position within the number and its base, which is 8 in the case of octal.

Allowing the digit “9” in octal would create ambiguity because it would be unclear whether it represents 9 in decimal or a different value in octal. To avoid confusion and maintain consistency within the base-8 system, only the digits 0 through 7 are used in octal notation.

What is 163.875 base 10 in binary?

To convert the decimal number 163.875 to binary:

1. Convert the integer part (163) to binary:
   • 163 ÷ 2 = 81 remainder 1
   • 81 ÷ 2 = 40 remainder 1
   • 40 ÷ 2 = 20 remainder 0
   • 20 ÷ 2 = 10 remainder 0
   • 10 ÷ 2 = 5 remainder 0
   • 5 ÷ 2 = 2 remainder 1
   • 2 ÷ 2 = 1 remainder 0
   • 1 ÷ 2 = 0 remainder 1

Read the remainders in reverse order to get the binary representation: 10100011.

2. Convert the fractional part (0.875) to binary:
   • Multiply the fractional part by 2 to get the next binary digit.
   • 0.875 * 2 = 1.75 (First digit after the binary point is 1)
   • Take the fractional part and repeat the process:
     • 0.75 * 2 = 1.5 (Next digit is 1)
     • 0.5 * 2 = 1.0 (Next digit is 1)

Combine the binary digits: 0.111.

3. Combine the integer and fractional parts: 10100011.111

So, 163.875 in base 10 is equal to 10100011.111 in binary.

How do you convert 0.513 base 10 to octal?

To convert the decimal number 0.513 to octal, you can convert the fractional part separately and then combine it with the integer part.

1. Convert the integer part (0) to octal: It remains as 0 in octal.
2. Convert the fractional part (0.513) to octal:
   • Multiply the fractional part by 8 to get the next octal digit.
   • 0.513 * 8 = 4.104 (First digit after the octal point is 4)
   • Take the fractional part and repeat the process:
     • 0.104 * 8 = 0.832 (Next digit is 0)
     • 0.832 * 8 = 6.656 (Next digit is 6)
     • 0.656 * 8 = 5.248 (Next digit is 5)

Combine the octal digits: 0.413625.

3. Combine the integer and fractional parts: 0.413625

So, 0.513 in base 10 is equal to 0.413625 in octal.

What is 0.6875 base 10 in binary?

To convert the decimal number 0.6875 to binary, you can convert the fractional part separately and then combine it with the integer part.

1. Convert the integer part (0) to binary: It remains as 0 in binary.
2. Convert the fractional part (0.6875) to binary:
   • Multiply the fractional part by 2 to get the next binary digit.
   • 0.6875 * 2 = 1.375 (First digit after the binary point is 1)
   • Take the fractional part and repeat the process:
     • 0.375 * 2 = 0.75 (Next digit is 0)
     • 0.75 * 2 = 1.5 (Next digit is 1)
     • 0.5 * 2 = 1.0 (Next digit is 1)

Combine the binary digits: 0.1011.

3. Combine the integer and fractional parts: 0.1011

So, 0.6875 in base 10 is equal to 0.1011 in binary.

What decimal number is represented by 11111111 in binary code?

The binary number 11111111 represents the decimal number 255. Each digit in the binary number corresponds to a power of 2, with the rightmost digit representing 2^0 (1), the next digit representing 2^1 (2), the next 2^2 (4), and so on. Adding up these powers of 2 results in the decimal value 255:

2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.

So, the binary number 11111111 is equal to 255 in decimal.