Convert (412)10 to i) Binary ii) Octal iii) Hexadecimal

Conversion of Decimal to Binary

To convert a decimal number to binary, you divide the number by 2 and write down the remainder. You then take the quotient from that division and divide it by 2 again, writing down the remainder. You continue this process until the quotient is 0. The binary number is then the remainders read in reverse order.

Step-by-Step Conversion of (412)10 to Binary:

1. Divide 412 by 2, quotient is 206, remainder is 0.
2. Divide 206 by 2, quotient is 103, remainder is 0.
3. Divide 103 by 2, quotient is 51, remainder is 1.
4. Divide 51 by 2, quotient is 25, remainder is 1.
5. Divide 25 by 2, quotient is 12, remainder is 1.
6. Divide 12 by 2, quotient is 6, remainder is 0.
7. Divide 6 by 2, quotient is 3, remainder is 0.
8. Divide 3 by 2, quotient is 1, remainder is 1.
9. Divide 1 by 2, quotient is 0, remainder is 1.

Now, read the remainders in reverse order to get the binary number: 110011100.

Conversion of Decimal to Octal

To convert a decimal number to octal, you divide the number by 8 and write down the remainder. You then take the quotient from that division and divide it by 8 again, writing down the remainder. You continue this process until the quotient is 0. The octal number is then the remainders read in reverse order.

Step-by-Step Conversion of (412)10 to Octal:

1. Divide 412 by 8, quotient is 51, remainder is 4.
2. Divide 51 by 8, quotient is 6, remainder is 3.
3. Divide 6 by 8, quotient is 0, remainder is 6.

Now, read the remainders in reverse order to get the octal number: 634.

Conversion of Decimal to Hexadecimal

To convert a decimal number to hexadecimal, you divide the number by 16 and write down the remainder. You then take the quotient from that division and divide it by 16 again, writing down the remainder. You continue this process until the quotient is 0. The hexadecimal number is then the remainders read in reverse order. Note that in hexadecimal, numbers 10-15 are represented by letters A-F.

Step-by-Step Conversion of (412)10 to Hexadecimal:

1. Divide 412 by 16, quotient is 25, remainder is 12 (which is 'C' in hexadecimal).
2. Divide 25 by 16, quotient is 1, remainder is 9.
3. Divide 1 by 16, quotient is 0, remainder is 1.

Now, read the remainders in reverse order to get the hexadecimal number: 19C.

Summary Table

Base	Conversion Process	Result
Binary	Divide by 2	110011100
Octal	Divide by 8	634
Hexadecimal	Divide by 16	19C

Examples

Here are the examples of the conversion process for the decimal number 412:

Decimal to Binary:

Step 1: 412 ÷ 2 = 206 remainder 0
Step 2: 206 ÷ 2 = 103 remainder 0
Step 3: 103 ÷ 2 = 51 remainder 1
Step 4: 51 ÷ 2 = 25 remainder 1
Step 5: 25 ÷ 2 = 12 remainder 1
Step 6: 12 ÷ 2 = 6 remainder 0
Step 7: 6 ÷ 2 = 3 remainder 0
Step 8: 3 ÷ 2 = 1 remainder 1
Step 9: 1 ÷ 2 = 0 remainder 1
Binary: 110011100

Decimal to Octal:

Step 1: 412 ÷ 8 = 51 remainder 4
Step 2: 51 ÷ 8 = 6 remainder 3
Step 3: 6 ÷ 8 = 0 remainder 6
Octal: 634

Decimal to Hexadecimal:

Step 1: 412 ÷ 16 = 25 remainder 12 (C)
Step 2: 25 ÷ 16 = 1 remainder 9
Step 3: 1 ÷ 16 = 0 remainder 1
Hexadecimal: 19C

These are the binary, octal, and hexadecimal equivalents of the decimal number 412.