The binary number 11111111 represents the decimal number 255.
Binary is a base-2 numeral system that uses only two symbols, 0 and 1. It is the fundamental language of computers, where each digit (called a bit) corresponds to an electrical signal being off (0) or on (1). To understand what 11111111 means, we convert it from binary to its decimal equivalent.
Converting Binary to Decimal
Converting a binary number to its decimal form involves summing the products of each binary digit and its corresponding power of 2. For an 8-bit binary number, which is commonly referred to as a byte, the positions from right to left correspond to increasing powers of 2, starting from $2^0$.
Let's break down the binary number 11111111:
| Binary Digit | Position (from right, starting at 0) | Positional Value (Power of 2) | Calculation | Decimal Contribution |
|---|---|---|---|---|
| 1 | 7 | $2^7 = 128$ | $1 \times 128$ | 128 |
| 1 | 6 | $2^6 = 64$ | $1 \times 64$ | 64 |
| 1 | 5 | $2^5 = 32$ | $1 \times 32$ | 32 |
| 1 | 4 | $2^4 = 16$ | $1 \times 16$ | 16 |
| 1 | 3 | $2^3 = 8$ | $1 \times 8$ | 8 |
| 1 | 2 | $2^2 = 4$ | $1 \times 4$ | 4 |
| 1 | 1 | $2^1 = 2$ | $1 \times 2$ | 2 |
| 1 | 0 | $2^0 = 1$ | $1 \times 1$ | 1 |
| Total | 255 |
By summing all the decimal contributions ($128 + 64 + 32 + 16 + 8 + 4 + 2 + 1$), we arrive at the total decimal value of 255.
Significance of 255 in Computing
The decimal number 255, represented by 11111111 in binary, holds significant importance in various areas of computing due to its status as the maximum value representable by an 8-bit unsigned integer:
- Data Representation: An 8-bit unsigned integer can store values from 0 (00000000 binary) to 255 (11111111 binary), providing a total of 256 unique possibilities.
- Networking (IPv4 Addresses): In IPv4 addresses (e.g., 192.168.1.1), each of the four segments (octets) can range from 0 to 255. For instance, a broadcast address often uses 255 in its host portion (e.g., 192.168.1.255).
- Digital Graphics (RGB Color Model): In the widely used RGB color model for digital displays, the intensity of red, green, and blue components is often expressed using an 8-bit value, ranging from 0 (no intensity) to 255 (full intensity). For example, pure white is (255, 255, 255), and pure black is (0, 0, 0).
- Subnet Masks: In computer networking, subnet masks frequently use 255 to denote network portions of an IP address. For instance, 255.255.255.0 indicates that the first three octets specify the network address, with the last octet reserved for host addresses within that network.
Understanding how binary numbers convert to decimal is foundational for anyone working with or learning about digital systems and computer programming. For more comprehensive details on this process, you can explore resources on how to convert binary into decimal.
