Samantha NicoleThe binary number 01010 converts to the decimal number 10.
To convert binary 01010 to decimal, each digit is multiplied by 2 raised to its position power, starting from 0 on the right. Summing these gives the decimal value. In this case, 0×2^4 + 1×2^3 + 0×2^2 + 1×2^1 + 0×2^0 results in 10.
Binary to Decimal Conversion
Binary numbers are composed of 0s and 1s. Each position in the binary number has a weight, which is a power of 2. The rightmost position is 2^0, then moving left, 2^1, 2^2, and so on. To convert, multiply each binary digit by its position’s weight, then add all the results.
Conversion Tool
Result in decimal:
Conversion Formula
The formula to convert binary to decimal is sum of each binary digit multiplied by 2 raised to its position index, starting from 0 on the right. For example, for binary 01010, calculations are: (0×2^4) + (1×2^3) + (0×2^2) + (1×2^1) + (0×2^0). This sums to 8 + 2 = 10.
This works because every binary digit indicates whether a specific power of 2 is included in the total. Digits of 1 add the value of their position, while 0s contribute nothing. The sum combines these to produce the decimal equivalent.
Conversion Example
- Binary: 1011
- Step 1: Write down positional values: 2^3, 2^2, 2^1, 2^0
- Step 2: Multiply each binary digit by its position’s value: 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0
- Step 3: Calculate: 8 + 0 + 2 + 1
- Step 4: Sum all: 8 + 0 + 2 + 1 = 11
- Result: Binary 1011 equals decimal 11
Conversion Chart
| Binary | Decimal |
|---|---|
| 11111001 | 985 |
| 11111010 | 986 |
| 11111011 | 987 |
| 11111100 | 988 |
| 11111101 | 989 |
| 11111110 | 990 |
| 11111111 | 991 |
| 100000000 | 256 |
| 100000001 | 257 |
| 100000010 | 258 |
| 100000011 | 259 |
| 100000100 | 260 |
| 100000101 | 261 |
| 100000110 | 262 |
| 100000111 | 263 |
| 100001000 | 264 |
| 100001001 | 265 |
| 100001010 | 266 |
| 100001011 | 267 |
| 100001100 | 268 |
| 100001101 | 269 |
| 100001110 | 270 |
| 100001111 | 271 |
| 100010000 | 272 |
| 100010001 | 273 |
| 100010010 | 274 |
| 100010011 | 275 |
| 100010100 | 276 |
| 100010101 | 277 |
| 100010110 | 278 |
| 100010111 | 279 |
Use this chart to quickly find decimal equivalents for binary values within this range. Read the binary number on the left, then look across to find its decimal equivalent.
Related Conversion Questions
- How do I convert binary 01010 to decimal without a calculator?
- What is the decimal value of binary 01010 in different number systems?
- Can I convert binary 01010 to hexadecimal directly?
- What is the binary equivalent of decimal 10?
- How does leading zero affect binary to decimal conversion?
- Is binary 01010 the same as 1010 in decimal calculations?
- What are some common mistakes when converting binary to decimal?
Conversion Definitions
Binary
Binary is a number system that uses only two digits, 0 and 1, representing values in base 2. It is the fundamental language of computers, where each digit corresponds to an off or on state in electronic circuits, enabling digital processing and storage.
Decimal
Decimal is a base-10 number system that employs ten digits from 0 to 9. It is the most familiar system used in everyday life, representing values by combining these digits with positional weights, where each position corresponds to a power of 10.
Conversion FAQs
How do I verify that my binary to decimal conversion is correct?
To verify, reapply the conversion formula by summing each binary digit times 2 raised to its position power. Cross-check the result with a calculator or conversion table. Also, converting back from decimal to binary can confirm accuracy.
Why do leading zeros in binary numbers not affect the decimal value?
Leading zeros add no value because they do not contribute to the sum of the weighted powers. They are simply placeholders, making the binary number look longer but not changing its actual value in decimal form.
What is the significance of the most significant bit in binary numbers?
The most significant bit (MSB) is the leftmost digit in a binary number. It indicates the highest value position, and in unsigned numbers, it has the greatest weight. Its value influences the overall size of the number significantly.
Can I convert binary numbers to other bases, like octal or hexadecimal, directly?
Yes, binary numbers can be converted directly into octal or hexadecimal by grouping bits. For hexadecimal, group bits in fours from right to left. For octal, group bits in threes. Each group then maps to its corresponding digit in the target base.
