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Decimal to Binary Converter



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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.