Binary to Decimal Converter

Convert binary numbers to decimal, hexadecimal, and octal with step-by-step explanations showing positional values and grouping methods.

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Quick presets

Pro Tips

  • Quick multiply/divide by 2: Left-shift doubles a binary number; right-shift halves it.
  • Check parity: AND a number with 1. If result is 1, it is odd. If 0, it is even.
  • Hex shortcut: Each hex digit maps to exactly 4 binary bits (nibble). F = 1111, A = 1010.
  • Two's complement: To negate a binary number, invert all bits and add 1.
  • XOR swap: You can swap two values using three XOR operations without a temp variable.

Last updated: March 2026

What Is the Binary to Decimal Converter?

This tool converts binary numbers to decimal, hexadecimal, and octal instantly. Enter a binary value and see all base representations with step-by-step positional value calculations. You can also convert from decimal, octal, or hex back to binary.

Binary to decimal conversion is one of the most common tasks in computer science coursework. Understanding how positional notation works in base 2 is fundamental to grasping how computers store and process numbers.

How Binary to Decimal Conversion Works

Step 1: Write out the binary number and assign each digit a power of 2, starting from 2⁰ on the right.

Step 2: Multiply each binary digit (0 or 1) by its corresponding power of 2.

Step 3: Add all the products together. The sum is the decimal equivalent.

For example, binary 10110 = (1×16) + (0×8) + (1×4) + (1×2) + (0×1) = 22 in decimal.

Common Binary to Decimal Conversions

Memorizing a few key values helps with quick mental conversion: 1 = 1, 10 = 2, 100 = 4, 1000 = 8, 10000 = 16, 100000 = 32, 1000000 = 64, 10000000 = 128, 11111111 = 255. These are powers of 2, and every binary number is a combination of these values.

Key milestone values include 256 (2⁸, one byte), 1024 (2¹⁰, one kilobyte), 65536 (2¹⁶, two bytes), and 4294967296 (2³², four bytes or one 32-bit word).

Frequently Asked Questions

How do you convert binary to decimal?

Multiply each binary digit by its positional power of 2, then sum the results. For example, 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal. The rightmost bit is 2⁰ = 1, the next is 2¹ = 2, and so on.

What is binary 1111 in decimal?

Binary 1111 = (1×8) + (1×4) + (1×2) + (1×1) = 15 in decimal. This is also F in hexadecimal and 17 in octal.

What is the largest 8-bit binary number?

The largest unsigned 8-bit number is 11111111, which equals 255 in decimal (2⁸ - 1). For signed 8-bit (two's complement), the range is -128 to 127.

How do you convert decimal to binary?

Repeatedly divide the decimal number by 2 and record the remainders. Read the remainders from bottom to top. For example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1. Reading bottom-to-top: 1101.

What is 255 in binary?

255 in binary is 11111111 (eight 1s). This is the maximum value of an unsigned 8-bit byte. It is also FF in hexadecimal and 377 in octal.

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