The radix of binary number is

Explanation:

The Radix of a Binary Number

Definition: In numerical systems, the term "radix" refers to the base of a number system. It is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, the decimal system has a radix of 10 because it uses 10 unique digits (0 through 9).

Radix of Binary Numbers: The binary number system is a numeral system that uses only two unique digits, 0 and 1. Hence, the radix of the binary number system is 2. Binary is the foundation of all modern computing systems and digital electronics because it aligns well with the two-state nature of electronic components (on and off).

Understanding Binary Numbers:

Binary numbers represent values using two symbols: 0 and 1. Each digit in a binary number is referred to as a "bit" (binary digit). The value of each position in a binary number is a power of 2, starting from the rightmost digit (least significant bit, or LSB) and increasing to the leftmost digit (most significant bit, or MSB). For example:

• The binary number 101 represents the decimal value: (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 4 + 0 + 1 = 5.

Practical Applications:

• The binary system is the basis of computer programming and hardware design. Computers process data in binary because it is easier to implement in digital circuits, where only two states are needed: on (1) and off (0).
• Binary is also used in data transmission, coding systems, and digital communication protocols.

Correct Option Analysis:

The correct option is:

Option 3: 2

This option correctly identifies the radix of a binary number system, which is 2. Binary numbers use only two unique symbols (0 and 1), making the radix or base of the system equal to 2.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 1

This option is incorrect because a radix of 1 would mean the numeral system uses only one unique digit. Such a system is not practical for representing numbers, as it would fail to distinguish between different values.

Option 2: 0

This option is incorrect because a radix of 0 is not defined or meaningful in numeral systems. A base of 0 would imply no symbols are available for representing numbers, which is impossible.

Option 4: 8

This option is incorrect because a radix of 8 corresponds to the octal numeral system, not the binary system. The octal system uses eight unique digits (0 through 7) to represent numbers.

Option 5: No answer provided

While this option is left blank, the correct answer remains option 3, as explained above.

Conclusion:

The radix of the binary number system is 2, reflecting the two unique digits (0 and 1) used to represent numbers. Understanding the concept of radix is crucial for working with various numeral systems, including binary, decimal, octal, and hexadecimal. This knowledge is fundamental in computing, electronics, and digital communication, where binary plays a pivotal role.