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Convert The Following Unsigned Binary Numbers to Decimal Calculator

Reviewed by Calculator Editorial Team

Convert unsigned binary numbers to decimal with our free online calculator. Learn the binary to decimal conversion process with step-by-step examples.

How to Convert Binary to Decimal

Binary numbers are base-2 numbers that use only two digits: 0 and 1. Decimal numbers are base-10 numbers that use digits 0 through 9. Converting binary to decimal involves understanding the positional values of each binary digit.

Step-by-Step Conversion Process

  1. Write down the binary number with each digit in its positional place.
  2. Starting from the right (which is the least significant bit), assign each digit a power of 2 based on its position (starting with 0).
  3. Multiply each binary digit by 2 raised to the power of its position.
  4. Sum all the values to get the decimal equivalent.

Remember: Binary numbers are unsigned when they don't have a sign bit. This calculator handles only positive binary numbers.

Binary to Decimal Conversion Formula

The general formula for converting an n-bit binary number to decimal is:

Decimal = bn-1 × 2n-1 + bn-2 × 2n-2 + ... + b1 × 21 + b0 × 20

Where bn-1, bn-2, ..., b0 are the binary digits (0 or 1).

For example, the binary number 1011 would be converted as:

1 × 23 + 0 × 22 + 1 × 21 + 1 × 20 = 8 + 0 + 2 + 1 = 11

Conversion Examples

Let's look at several examples of binary to decimal conversion:

Example 1: 8-bit Binary Number

Convert 11010110 to decimal:

1 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20

= 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0 = 214

Example 2: 4-bit Binary Number

Convert 1010 to decimal:

1 × 23 + 0 × 22 + 1 × 21 + 0 × 20

= 8 + 0 + 2 + 0 = 10

Example 3: 16-bit Binary Number

Convert 1111111111111111 to decimal:

This is the maximum value for a 16-bit unsigned binary number.

1 × 215 + 1 × 214 + ... + 1 × 20 = 65535

Frequently Asked Questions

What is the difference between signed and unsigned binary numbers?

Unsigned binary numbers represent only positive values, while signed binary numbers can represent both positive and negative values. The most significant bit (leftmost bit) in signed numbers is used as the sign bit (0 for positive, 1 for negative).

How many decimal digits are needed to represent an n-bit binary number?

An n-bit binary number can represent values from 0 to 2n-1. The number of decimal digits needed is floor(log10(2n-1)) + 1.

What is the largest decimal number that can be represented by an 8-bit unsigned binary number?

The largest 8-bit unsigned binary number is 11111111, which converts to 255 in decimal.

Can this calculator handle binary numbers with leading zeros?

Yes, this calculator will correctly convert binary numbers with leading zeros by treating them as part of the number's positional value.