ConvertOnlineDecimal to Binary
This converter converts the given decimal number to binary.
Decimal to Binary
Converting a Decimal Number to Binary
Binary numbers are fundamental in computing and digital electronics. The binary numeral system represents numeric values using two symbols: 0 and 1. Each digit in a binary number is called a bit.
To convert a decimal number (base 10) to binary (base 2), we repeatedly divide the number by 2 and record the remainder. The binary equivalent is obtained by reading the remainders in reverse order, starting from the last division.
Examples
Let's go through some examples to understand how to convert decimal numbers to their binary equivalents.
1. Convert the decimal number 13 to binary.
Answer
First, we identify the given number:
Given:
- Decimal: 13
Next, we divide the number by 2, recording the quotient and remainder at each step:
Steps:
- 13 ÷ 2 = 6, remainder = 1
- 6 ÷ 2 = 3, remainder = 0
- 3 ÷ 2 = 1, remainder = 1
- 1 ÷ 2 = 0, remainder = 1
We then read the remainders from bottom to top:
Binary Equivalent:
1101
Result:
∴ The binary equivalent of the decimal number 13 is 1101.
2. Convert the decimal number 7 to binary.
Answer
We start by identifying the number:
Given:
- Decimal: 7
Next, we divide the number by 2, recording the quotient and remainder at each step:
Steps:
- 7 ÷ 2 = 3, remainder = 1
- 3 ÷ 2 = 1, remainder = 1
- 1 ÷ 2 = 0, remainder = 1
We then read the remainders from bottom to top:
Binary Equivalent:
111
Result:
∴ The binary equivalent of the decimal number 7 is 111.
3. Determine the binary equivalent of the decimal number 20.
Answer
First, we identify the given number:
Given:
- Decimal: 20
Next, we divide the number by 2, recording the quotient and remainder at each step:
Steps:
- 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
We then read the remainders from bottom to top:
Binary Equivalent:
10100
Result:
∴ The binary equivalent of the decimal number 20 is 10100.
4. Convert the decimal number 5 to binary.
Answer
We start by identifying the number:
Given:
- Decimal: 5
Next, we divide the number by 2, recording the quotient and remainder at each step:
Steps:
- 5 ÷ 2 = 2, remainder = 1
- 2 ÷ 2 = 1, remainder = 0
- 1 ÷ 2 = 0, remainder = 1
We then read the remainders from bottom to top:
Binary Equivalent:
101
Result:
∴ The binary equivalent of the decimal number 5 is 101.