The binary number 10101010 equals 170 in decimal. This conversion involves understanding each binary digit’s positional value and summing these based on whether the digit is 1 or 0.
Binary to Decimal Conversion
The process of converting binary to decimal involves multiplying each binary digit by 2 raised to the power of its position, counting from right to left starting at 0. When the digit is 1, the value adds to the total, when 0, it skips that position.
Result in decimal:
Conversion Formula
The formula for binary to decimal is sum of each binary digit multiplied by 2 raised to its position index, starting from 0 on the right. It works because each position represents a power of 2. For example, in 10101010:
1×2^7 = 128
0×2^6 = 0
1×2^5 = 32
0×2^4 = 0
1×2^3 = 8
0×2^2 = 0
1×2^1 = 2
0×2^0 = 0
Add these up: 128 + 32 + 8 + 2 = 170.
Conversion Example
Binary: 1101
Step 1: Write down each digit with its position: 1(3), 1(2), 0(1), 1(0)
Use this chart to quickly find decimal equivalents for binary numbers around 10101010, fostering quick reference and comparison.
Related Conversion Questions
How do I convert 10101010 binary to decimal manually?
What is the decimal value of binary 10101010?
Can you show me step-by-step how 10101010 becomes 170 in decimal?
What is the process to convert binary 10101010 into base 10?
What decimal number does binary 10101010 represent?
How to verify that binary 10101010 equals 170 in decimal?
Are there quick methods for converting binary to decimal for 8-bit numbers like 10101010?
Conversion Definitions
Binary
Binary is a number system that uses only two digits, 0 and 1, to represent all numbers. It forms the basis for digital computing, where each digit is called a bit, and combinations of bits encode data in electronic devices.
Decimal
Decimal is a base-10 number system utilizing ten digits from 0 to 9. It is the standard system for counting and arithmetic in everyday life, where each position represents a power of ten, making it familiar and easy to understand.
Conversion FAQs
How does binary 10101010 compare to other binary numbers in terms of value?
Binary 10101010 is relatively high among 8-bit numbers because it has high-value bits set to 1 at positions 7, 5, 3, and 1, summing to 170 in decimal. It is larger than, for example, 10100001 (which equals 161) but less than 11111111 (which equals 255).
Is there a shortcut to convert binary 10101010 without calculating each position?
For quick conversion, recognize patterns or use calculator tools. But manually, summing the powers of 2 at positions where bits are 1 is fastest. For 10101010, adding 128, 32, 8, and 2 gives 170, which is straightforward once familiar with the pattern.
What are common mistakes when converting binary like 10101010 into decimal?
Mistakes include miscounting positions, confusing the order of bits, or adding the wrong powers of two. Also, forgetting to only add when the bit is 1, or mixing up the base-2 and base-10 calculations, can lead to incorrect results.
