Decimal to Binary

Convert decimal numbers to binary quickly with our Decimal to Binary Converter. Ideal for computer science and digital systems, ensuring accurate conversions.

Decimal to Binary

Decimal Number Definition:A decimal number is a number expressed in the base-ten numerical system. It uses ten symbols—0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—to represent quantities. Each digit's position in a decimal number corresponds to a power of 10.

Decimal Number Example:The number 4567 is a decimal number. In this number, 4 is in the thousands place, 5 is in the hundreds place, 6 is in the tens place, and 7 is in the ones place.

Binary Number Definition:A binary number is a number expressed in the base-two numerical system. It uses two symbols—0 and 1—to represent quantities. Each digit's position in a binary number corresponds to a power of 2.

Binary Number Example:The binary number 10110 is an example. In this number, 1 is in the 16s place (2^4), 0 is in the 8s place (2^3), 1 is in the 4s place (2^2), 1 is in the 2s place (2^1), and 0 is in the 1s place (2^0). When converted to decimal, this binary number represents the decimal number 22.

Conversion Process: Decimal to Binary

  1. Divide by 2: Begin by dividing the decimal number by 2.
  2. Record Remainders: Record the remainder (either 0 or 1) after each division. These remainders will form the binary digits.
  3. Repeat Division: Continue dividing the quotient by 2 until the quotient becomes 0.
  4. Reverse the Remainders: Once all divisions are done, the binary digits obtained are reversed to get the final binary number.

Example: Convert Decimal 27 to Binary

Step 1: 272=13\frac{27}{2} = 13 Remainder 1
Step 2: 132=6\frac{13}{2} = 6 Remainder 1
Step 3: 62=3\frac{6}{2} = 3 Remainder 0
Step 4: 32=1\frac{3}{2} = 1 Remainder 1
Step 5: 12=0\frac{1}{2} = 0 Remainder 1

Reversing the remainders, we get 11011. Therefore, the binary representation of decimal number 27 is 11011.

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