Shift from Radix 16 to Radix 2: Switch from Base 16 to Base 2

This updated guide examines Shift from Radix 16 to Radix 2: Switch from Base 16 to Base 2 and organizes the essential facts, background, and practical takeaways in clear American English.

16-base system (hexadecimal)

Base 2 system (binary system)

The binary system uses two characters, 0 and 1, to represent a value.

Binary systems were applied in ancient Egypt, China and India for many different purposes. In the modern world, binary has become the language of electronic science and computers. This is the most efficient system for detecting electrical signals: Turn off ( 0 ) and turn on ( 1 ). It is also the basis for the binary code used to compose data on the computer. Even the digital text you are currently reading also includes binary numbers.

Reading some binary is easier than you think. This is a quantitative position-based system, so each digit in a binary number is raised to powers 2, starting from the rightmost position of 2⁰. In base 2 system, each binary digit refers to 1 bit.

How to read binary numbers

To convert binary to decimal, some basic knowledge of how to read binary numbers can help. As mentioned above, in binary counting using quantitative positions, each bit (binary digit) is a power of 2. This means that all binary numbers can be expressed in terms of power of 2, with the rightmost position is 2₀.

For example, binary numbers (1010)₂can also be written as follows:

(1 * 2³) + (0 * 2²) + (1 * 2¹) + (0 * 2⁰)

Example of conversion from base 16 to base 2

• (1E3)₁₆= (0001 1110 0011)₂
• (0A2B)₁₆= (0000 1010 0010 1011)₂
• (7E0C)₁₆= (0111 1110 0000 1100)₂

Conversion table from base 16 to base 2

Mechanical number 16Circular number 200000100012001030011401005010160110701118100091001A1010B1011C1100D1101E1110F1111