The binary number 01010 converts to 10 in decimal form.
To convert 01010 binary to decimal, each digit is multiplied by 2 raised to the position power, counting from right to left starting at 0. Summing these values gives the decimal equivalent. For example, the second digit from the right is multiplied by 2^1, the third by 2^2, and so on, then added together.
Binary to Decimal Conversion
Result in decimal:
Conversion Formula
The conversion from binary to decimal uses the formula: sum of each binary digit multiplied by 2 raised to the power of its position, starting from 0 at the rightmost digit. For example, binary 1010 is calculated as (1×2^3) + (0×2^2) + (1×2^1) + (0×2^0). This works because each position represents a power of 2, making the binary system a base-2 numeral system.
In the case of 01010, the calculation is: (0×2^4) + (1×2^3) + (0×2^2) + (1×2^1) + (0×2^0) = 0 + 8 + 0 + 2 + 0 = 10.
Conversion Example
- Convert binary 1101:
- Write down binary digits: 1 1 0 1
- Starting from right, assign powers of 2: 2^0, 2^1, 2^2, 2^3
- Calculate: (1×2^3) + (0×2^2) + (1×2^1) + (1×2^0)
- Compute: 8 + 0 + 2 + 1 = 11
- Convert binary 1001:
- Digits: 1 0 0 1
- Calculate: (1×2^3) + (0×2^2) + (0×2^1) + (1×2^0)
- Result: 8 + 0 + 0 + 1 = 9
- Convert binary 1110:
- Digits: 1 1 1 0
- Calculate: (1×2^3) + (1×2^2) + (1×2^1) + (0×2^0)
- Result: 8 + 4 + 2 + 0 = 14
Conversion Chart
| Binary | Decimal |
|---|---|
| 11111001 | 249 |
| 11111010 | 250 |
| 11111011 | 251 |
| 11111100 | 252 |
| 11111101 | 253 |
| 11111110 | 254 |
| 11111111 | 255 |
| 1000000001 | 513 |
| 1000000010 | 514 |
| 1000000011 | 515 |
| 1000000100 | 516 |
| 1000000101 | 517 |
| 1000000110 | 518 |
| 1000000111 | 519 |
| 1000001000 | 520 |
| 1000001001 | 521 |
| 1000001010 | 522 |
| 1000001011 | 523 |
| 1000001100 | 524 |
| 1000001101 | 525 |
| 1000001110 | 526 |
| 1000001111 | 527 |
| 1000010000 | 528 |
| 1000010001 | 529 |
| 1000010010 | 530 |
| 1000010011 | 531 |
| 1000010100 | 532 |
| 1000010101 | 533 |
| 1000010110 | 534 |
| 1000010111 | 535 |
| 1000011000 | 536 |
| 1000011001 | 537 |
| 1000011010 | 538 |
| 1000011011 | 539 |
| 1000011100 | 540 |
| 1000011101 | 541 |
| 1000011110 | 542 |
| 1000011111 | 543 |
| 1000100000 | 544 |
| 1000100001 | 545 | … |
Use this chart to find the decimal value that corresponds to a binary number within the range. Read the binary in the first column and match it to the decimal in the second to understand the conversion.
Related Conversion Questions
- How do I convert binary 01010 to decimal manually?
- What is the decimal equivalent of binary 01010 in different numeral systems?
- Can I use a calculator to convert binary 01010 to decimal automatically?
- Why does binary 01010 equal 10 in decimal?
- What are common mistakes when converting binary 01010 to decimal?
- How does leading zero in binary number 01010 affect the decimal conversion?
- Is binary 01010 the same as binary 1010 in decimal?
Conversion Definitions
Binary
Binary is a base-2 numeral system using only two digits: 0 and 1. It represents data in digital electronics, where each digit corresponds to an off or on state in a circuit, making it fundamental for computing processes, coding, and digital communications.
Decimal
Decimal is a base-10 counting system, using ten digits from 0 to 9. It is the most common numeral system for daily arithmetic, representing quantities, and basic calculations, where each digit's position indicates its value multiplied by powers of 10.
Conversion FAQs
Can I convert binary 01010 to decimal without a calculator?
Yes, by multiplying each binary digit by 2 raised to its position power and summing all the results, you can convert 01010 to decimal manually. For example, 0×2^4 + 1×2^3 + 0×2^2 + 1×2^1 + 0×2^0 = 10.
What happens if I enter invalid characters in the binary input field?
If non-binary characters like letters or symbols are entered, the conversion script detects invalid input and displays an error message, preventing incorrect results. It's crucial to only input 0s and 1s for valid binary conversion.
Why does the conversion from binary to decimal use powers of 2?
Because binary is a base-2 system, each position in the number represents a power of 2. The rightmost digit is 2^0, the next is 2^1, and so forth, which allows the conversion to decimal by summing these weighted contributions.