The decimal equivalent of the binary number 1001111 is 79.
Understanding Binary to Decimal Conversion
Binary is a base-2 number system, meaning it only uses two digits: 0 and 1. In contrast, the decimal system (base-10) uses ten digits from 0 to 9. To convert a binary number to its decimal equivalent, we use the place value method, where each digit's position corresponds to a specific power of 2.
The Place Value Method
Each digit in a binary number has a "place value" that is a power of 2, starting from $2^0$ (which is 1) for the rightmost digit, and increasing as you move left.
To convert 1001111 from binary to decimal:
- Identify the binary digits: The number
1001111has seven digits. - Assign place values: Starting from the rightmost digit, assign powers of 2 (2^0, 2^1, 2^2, and so on).
- Multiply and sum: Multiply each binary digit by its corresponding place value and then sum all the results.
Let's break down the binary number 1001111:
| Binary Digit | Place Value (Power of 2) | Calculation | Result |
|---|---|---|---|
| 1 | $2^6 = 64$ | $1 \times 64$ | 64 |
| 0 | $2^5 = 32$ | $0 \times 32$ | 0 |
| 0 | $2^4 = 16$ | $0 \times 16$ | 0 |
| 1 | $2^3 = 8$ | $1 \times 8$ | 8 |
| 1 | $2^2 = 4$ | $1 \times 4$ | 4 |
| 1 | $2^1 = 2$ | $1 \times 2$ | 2 |
| 1 | $2^0 = 1$ | $1 \times 1$ | 1 |
Now, sum the results from the "Result" column:
$64 + 0 + 0 + 8 + 4 + 2 + 1 = 79$
Therefore, the decimal equivalent of the binary number 1001111 is 79.
Why is This Important?
Understanding how to convert between binary and decimal is fundamental in computer science and digital electronics. Computers process and store all information in binary form (as sequences of 0s and 1s), while humans typically interact with data in the more familiar decimal system. This conversion process is what allows us to interpret the binary data that computers use.
For more information on binary numbers and their conversion, you can refer to resources on binary numbers.
