The binary number 01010 converts to the decimal number 10.
To convert binary 01010 to decimal, each digit’s value is calculated by multiplying it with 2 raised to the position power, starting from 0 on the right. Adding these values gives the total decimal equivalent. In this case, 0×24 + 1×23 + 0×22 + 1×21 + 0×20 equals 8 + 0 + 2 + 0, which sums to 10.
Conversion Result
Conversion Tool
Result in decimal:
Conversion Formula
The conversion from binary to decimal involves summing each binary digit multiplied by 2 raised to the power of its position (starting from 0 on the right). This works because binary is a base-2 system, where each position represents a power of 2. For example, for 01010:
- 0×24 = 0
- 1×23 = 8
- 0×22 = 0
- 1×21 = 2
- 0×20 = 0
Adding these gives 0 + 8 + 0 + 2 + 0 = 10. This method works because each binary digit's value depends on its position, representing powers of 2.
Conversion Example
- Binary: 00101
- Step 1: Write down the positions: 4 3 2 1 0
- Step 2: Convert each digit with its power of 2:
- 0×24 = 0
- 0×23 = 0
- 1×22 = 4
- 0×21 = 0
- 1×20 = 1
- Step 3: Sum the values: 0 + 0 + 4 + 0 + 1 = 5
Conversion Chart
| Binary Value | Decimal Value |
|---|---|
| 1100010111 | 1031 |
| 1100011000 | 1032 |
| 1100011001 | 1033 |
| 1100011010 | 1034 |
| 1100011011 | 1035 |
| 11111000 | 248 |
| 11111111 | 255 |
| 100000000 | 256 |
| 101000000 | 320 |
| 110000000 | 384 |
| 111000000 | 448 |
| 1001100110 | 614 |
| 1010101010 | 682 |
| 1101010101 | 853 |
| 1010111100 | 700 |
| 1101110101 | 885 |
This chart helps you see the decimal equivalents of binary numbers in the range from 985.0 to 1035.0. Each row shows a binary value and its decimal counterpart, making it easier to compare and understand conversions visually.
Related Conversion Questions
- How do I convert binary 01010 to hexadecimal?
- What is the binary representation of the decimal number 10?
- Why does the binary 01010 equal 10 in decimal?
- Can I convert binary 01010 to octal easily?
- What are other binary numbers that convert to decimal 10?
- How to verify if a binary number is correct when converting to decimal?
- What is the process to convert a binary number to decimal without a calculator?
Conversion Definitions
Binary
Binary is a base-2 numeral system using only two digits, 0 and 1. It is used in digital electronics and computing because it directly corresponds to the on/off states of electronic switches. Each position represents a power of 2, starting from the rightmost digit.
Decimal
Decimal is a base-10 numeral system consisting of ten digits from 0 to 9. It is the standard numbering system used in everyday life, where each digit's position represents a power of 10. Numbers are formed by combining these digits based on place value.
Conversion FAQs
How can I quickly verify if my binary to decimal conversion is correct?
You can verify by reversing the process: convert the decimal back to binary and check if it matches the original binary number. Alternatively, use a calculator or online converter to compare results. Double-check each step for accuracy to avoid mistakes.
What tools are best for converting large binary numbers to decimal?
Using scientific calculators, programming languages like Python, or online conversion tools can handle large binary numbers efficiently. These tools perform the conversion instantly, reducing human error, especially with very long binary sequences.
Are there differences in converting binary to decimal for signed numbers?
Yes, signed binary numbers use specific formats like two's complement, which requires additional steps to interpret negative values. Unsigned binary numbers are straightforward, but signed ones involve considering the sign bit before conversion.