The binary number 01010 converts to the decimal number 10. This is because each digit in binary represents a power of 2, depending on its position.
To convert binary 01010 to decimal, we multiply each binary digit by 2 raised to its position index, starting from 0 on the right. Then, summing these values gives the decimal equivalent. For 01010, only the second and fourth positions contribute, resulting in 10.
Conversion Result
Binary 01010 equals decimal 10.
Conversion Tool
Result in decimal:
Conversion Formula
To change binary to decimal, each digit is multiplied by 2 raised to its position. Starting from right to left, position 0 is for the rightmost digit. Summing all these values gives the decimal. For example, in 01010, only the second and fourth bits are 1, so: (1×2^1)+(1×2^3)=2+8=10.
This process works because binary is a base-2 system, and each position represents a power of 2. By summing the products of each bit and its corresponding power, we accurately convert binary to decimal.
Conversion Example
- Binary: 1011
- Step 1: Write down the positions from right to left: 0, 1, 2, 3
- Step 2: Identify digits: 1 0 1 1
- Step 3: Multiply each digit by 2 raised to its position: (1×2^3)+(0×2^2)+(1×2^1)+(1×2^0)
- Step 4: Calculate each: (1×8)+(0×4)+(1×2)+(1×1)=8+0+2+1
- Step 5: Add all: 8+0+2+1=11
- Result: Binary 1011 equals decimal 11.
Conversion Chart
| Binary | Decimal |
|---|---|
| 11111001 | 985.0 |
| 11111010 | 986.0 |
| 11111011 | 987.0 |
| 11111100 | 988.0 |
| 11111101 | 989.0 |
| 11111110 | 990.0 |
| 11111111 | 991.0 |
| 100000000 | 256.0 |
| 100000001 | 257.0 |
| 100000010 | 258.0 |
| 100000011 | 259.0 |
| 100000100 | 260.0 |
| 100000101 | 261.0 |
| 100000110 | 262.0 |
| 100000111 | 263.0 |
| 100001000 | 264.0 |
| 100001001 | 265.0 |
| 100001010 | 266.0 |
| 100001011 | 267.0 |
| 100001100 | 268.0 |
| 100001101 | 269.0 |
| 100001110 | 270.0 |
| 100001111 | 271.0 |
| 100010000 | 272.0 |
| 100010001 | 273.0 |
| 100010010 | 274.0 |
| 100010011 | 275.0 |
| 100010100 | 276.0 |
| 100010101 | 277.0 |
| 100010110 | 278.0 |
| 100010111 | 279.0 |
Use this chart to quickly find decimal equivalents of binary numbers within this range. Just match the binary value and read off the decimal counterpart.
Related Conversion Questions
- How do I convert binary 01010 to hexadecimal?
- What is the binary equivalent of decimal 10?
- Can I convert binary 01010 into octal?
- What is the process to change binary 01010 to decimal manually?
- How does binary 01010 relate to ASCII characters?
- What are the common mistakes when converting binary 01010 to decimal?
- Is binary 01010 a valid input for digital systems?
Conversion Definitions
Binary
Binary is a base-2 number system using only two symbols, 0 and 1, to represent values in digital electronics and computing. Each digit's position indicates a power of 2, enabling efficient data storage and processing at the hardware level.
Decimal
Decimal is a base-10 number system using digits 0 through 9, widely used in everyday counting and calculations. It is positional, with each position representing a power of ten, making it intuitive for humans to interpret numeric data.
Conversion FAQs
How do I verify that 01010 in binary equals 10 in decimal?
To verify, convert each binary digit to its decimal value based on position. Multiply each 1 by 2 raised to its position index, sum all results, which gives 10. Cross-check by converting 10 back to binary, resulting in 01010, confirming the conversion.
Why are leading zeros in binary numbers like 01010 ignored in conversion?
Leading zeros do not affect the value because they contribute nothing to the sum. They are just placeholders, but the conversion process only considers digits with a '1' because zero times any power equals zero, which adds nothing.
What happens if I input a binary number with digits other than 0 or 1 into the tool?
The tool is designed to handle only binary digits; if you enter other digits, it may produce incorrect results or not work at all. Ensure only 0s and 1s are entered for accurate conversion. Invalid entries should be cleared or corrected before calculation.