Decimal to Binary
The decimal number system, also known as the base-10 system, is the most widely used number system for representing numbers. The binary number system, on the other hand, is a base-2 system and uses only two digits, 0 and 1, to represent numbers.
Converting a decimal number to its binary representation involves dividing the decimal number repeatedly by 2 and noting the remainders until the decimal number becomes zero. The remainders, read from bottom to top, give the binary representation of the decimal number.
What is the Decimal Number System?
The decimal number system, also known as the base-10 system, is a way of representing numbers using 10 symbols, 0 through 9. It is the most widely used number system and is used for everyday arithmetic and most scientific calculations.
In the decimal system, the value of a digit depends on its place value, with the rightmost digit having a place value of 1 and each digit to the left having a place value that is 10 times greater. For example, the decimal number 123 represents 1 * 100 + 2 * 10 + 3 * 1.
What is a Binary Number System?
The decimal number system, also known as the base-10 system, is a way of representing numbers using 10 symbols, 0 through 9. It is the most widely used number system and is used for everyday arithmetic and most scientific calculations.
In the decimal system, the value of a digit depends on its place value, with the rightmost digit having a place value of 1 and each digit to the left having a place value that is 10 times greater. For example, the decimal number 123 represents 1 * 100 + 2 * 10 + 3 * 1.
Decimal to Binary Conversion
Decimal to binary conversion involves converting a decimal number to its equivalent representation in the binary number system. This can be done by dividing the decimal number repeatedly by 2 and noting the remainders until the decimal number becomes zero. The remainders, read from bottom to top, give the binary representation of the decimal number.
How to Convert Decimal Numbers To Binary Numbers?
To convert a decimal number to binary, you can follow these steps:
- Divide the decimal number by 2 and keep track of the quotient and the remainder.
- Repeat step 1 with the quotient obtained from the previous step until the quotient is zero.
- Write down the remainders from step 1 in reverse order to obtain the binary representation of the decimal number.
For example, to convert the decimal number 12 to binary, the steps would be:
- 12 divided by 2 is 6 with a remainder of 0, so the binary representation so far is 0.
- 6 divided by 2 is 3 with a remainder of 0, so the binary representation so far is 00.
- 3 divided by 2 is 1 with a remainder of 1, so the binary representation so far is 100.
- 1 divided by 2 is 0 with a remainder of 1, so the binary representation so far is 1100, which is the final answer.
In Short, the binary representation of the decimal number 12 is 1100.
Decimal to Binary Table(0 to 9)
|
Decimal |
Binary |
|
0 |
0000 |
|
1 |
0001 |
|
2 |
0010 |
|
3 |
0011 |
|
4 |
0100 |
|
5 |
0101 |
|
6 |
0110 |
|
7 |
0111 |
|
8 |
1000 |
|
9 |
1001 |
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Frequently Asked Questions on Decimal to Binary
Convert the decimal fraction 0.66 to binary, the steps would be:
- 0.66 * 2 = 1.32, the whole number part is 1 and the fractional part is 0.32.
- 0.32 * 2 = 0.64, the whole number part is 0 and the fractional part is 0.64.
- 0.64 * 2 = 1.28, the whole number part is 1 and the fractional part is 0.28.
- 0.28 * 2 = 0.56, the whole number part is 0 and the fractional part is 0.56.
- 0.56 * 2 = 1.12, the whole number part is 1 and the fractional part is 0.12.
- 0.12 * 2 = 0.24, the whole number part is 0 and the fractional part is 0.24.
The repeating pattern of 0.24 * 2 = 0.48 * 2 = 0.96 * 2 = 1.92 * 2 = ... is recognized, so we can stop here. The binary representation of 0.66 is 0.101100110011001100..., where the sequence of binary digits after the decimal point is repeating.
To convert the decimal number 30 to binary, the steps would be:
- 30 divided by 2 is 15 with a remainder of 0, so the binary representation so far is 0.
- 15 divided by 2 is 7 with a remainder of 1, so the binary representation so far is 10.
- 7 divided by 2 is 3 with a remainder of 1, so the binary representation so far is 110.
- 3 divided by 2 is 1 with a remainder of 1, so the binary representation so far is 1110.
- 1 divided by 2 is 0 with a remainder of 1, so the binary representation so far is 11110, which is the final answer.
Therefore, the binary representation of the decimal number 30 is 11110.
The binary representation of the decimal number 8 is 1000.
The binary representation of 0.10 is 0.0001100110011001100..., where the sequence of binary digits after the decimal point is repeated.