The largest decimal integer that can be represented by an 8-bit unsigned binary number is 255.

The largest decimal integer that can be represented by an 8-bit unsigned binary number is 255. Let’s take a closer look at binary representation and why the largest decimal integer that can be represented in 8-bit binary is 255.

First of all, binary is a number system composed of 0 and 1, while decimal is a number system composed of numbers 0 to 9. In computer science, binary is the most basic representation of numbers because all data in computers is stored and processed in binary form.

An 8-bit binary number consists of 8 binary bits, each bit can be 0 or 1. Each bit of the binary bit represents a weight, and the weight increases from right to left, which are 1, 2, 4, 8, 16, 32, 64, and 128 (increasing in powers of 2).

Therefore, an 8-bit binary number, when all bits are 1, the largest decimal integer that can be represented is 255. This is because the highest bit of the 8-bit binary number is 128 (2 raised to the power of 7), and all the lower bits are 1, so the sum is 255. Beyond this value, more binary bits are needed to represent larger decimal integers.

The binary number system is a commonly used mathematical representation method in computers. In an 8-bit binary number, the maximum value is 255 because each bit of the 8-bit binary number represents a value with a different weight. The highest bit has a weight of 128 (that is, 2 to the 7th power), and the other bits have weights in sequence. It's 64, 32, 16, 8, 4, 2, 1.

When all bits are 1, the result of the bitwise weighted sum is 255, which is the largest decimal integer that can be represented by 8-bit binary. Therefore, the value of an 8-bit binary number ranges from 0 to 255, which is a maximum of 256 different numerical combinations. This relationship between the number of digits and the value range determines that the largest decimal integer that can be represented by 8-bit binary is 255.