10101010 Binary to Decimal – Answer with Formula

The binary number 10101010 converts to the decimal number 170.

This conversion is done by assigning each binary digit a power of 2 based on its position from right to left, starting at 0. Multiplying each digit by 2 raised to its position number and summing all results gives the decimal equivalent.

Binary 10101010 to Decimal Conversion

To convert the binary number 10101010 to decimal, we analyze each digit from right to left, multiply by the corresponding power of 2, and add all the values together. This process transforms the base-2 number into its base-10 counterpart.

Conversion Tool

Conversion Formula

The formula to convert binary to decimal involves summing each binary digit multiplied by 2 raised to the position index, starting from 0 on the right. For example, for 10101010:

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

Calculating each term:

• 128 + 0 + 32 + 0 + 8 + 0 + 2 + 0 = 170

This sum results in the decimal value 170, which is the equivalent of binary 10101010.

Conversion Example

• Binary: 1101
• Digits from right to left: 1, 0, 1, 1
• Step-by-step:
  • 1×2³ = 8
  • 0×2² = 0
  • 1×2¹ = 2
  • 1×2⁰ = 1
• Sum: 8 + 0 + 2 + 1 = 11

• Binary: 1110
• Digits: 0, 1, 1, 1
• Calculations:
  • 0×2³=0
  • 1×2²=4
  • 1×2¹=2
  • 1×2⁰=1
• Sum: 0+4+2+1=7

• Binary: 1001
• Digits: 1, 0, 0, 1
• Calculations:
  • 1×2³=8
  • 0×2²=0
  • 0×2¹=0
  • 1×2⁰=1
• Sum: 8+0+0+1=9

Conversion Chart

Use this chart to quickly find decimal equivalents for binary numbers in the range, by matching binary strings to corresponding decimal values.

Related Conversion Questions

• What is the decimal value of binary 10101010 if I change the last digit to 1?
• How do I convert binary 10101010 to hexadecimal?
• Can you show me the binary equivalent of decimal 170?
• What is the binary form of decimal 255?
• How do I convert binary 10101010 to octal?
• Why does binary 10101010 equal 170 in decimal?
• Is binary 10101010 a palindrome, and what is its decimal value?

Conversion Definitions

Binary

Binary is a numeral system that uses only two digits, 0 and 1, to represent numbers. It is the foundation of digital computing, where each digit (bit) signifies an on/off state. Binary numbers are used to encode data, instructions, and store information in computers.

Decimal

Decimal is a base-10 numbering system using digits 0 through 9. It is the most common system for human counting. Decimal numbers are composed of positions, each representing a power of 10, with the value determined by the digit and its position in the number.

Conversion FAQs

How does binary 10101010 relate to hexadecimal?

Binary 10101010 can be grouped into two sets of four bits: 1010 and 1010, which correspond to hexadecimal A and A, making the complete hexadecimal representation of 0xAA. This conversion simplifies reading binary data in compact form.

Why is binary important in computer systems?

Binary provides a simple way to represent on/off signals in electronic circuits. Computer hardware uses binary to process, store, and transmit data because digital circuits are naturally suited for binary states, ensuring reliability and efficiency in computations.

Can I convert binary 10101010 to other bases besides decimal and hexadecimal?

Yes, binary can be converted to octal (base-8) by grouping bits into threes, or to base-36 for more complex encoding schemes. Each conversion involves grouping bits and replacing them with equivalent digits in the target base, following specific rules.

What are common mistakes when converting binary to decimal?

Common mistakes include misaligning binary digits with their powers of 2, forgetting to include all positional values, or miscalculating the sum. It's crucial to process each digit from right to left, multiplying by the correct power, and summing accurately.