The decimal number 12 is written as 1100 in the binary number system. Binary, or base-2, is a numerical system that uses only two symbols: 0 and 1. This system is the foundational language for all digital circuits and computers, where these two digits represent the "off" and "on" states of electrical signals.
Understanding Decimal to Binary Conversion
Converting a decimal (base-10) number to a binary (base-2) number involves a systematic process of successive division by 2. Each division yields a quotient and a remainder. The binary representation is then formed by reading these remainders from the last one obtained to the first. This method effectively translates our everyday counting system into the language of computers.
Step-by-Step Conversion of 12 to Binary
To convert the decimal number 12 into its binary equivalent, follow these simple steps:
- Divide 12 by 2:
- 12 ÷ 2 = 6 with a remainder of 0
- Divide the quotient (6) by 2:
- 6 ÷ 2 = 3 with a remainder of 0
- Divide the quotient (3) by 2:
- 3 ÷ 2 = 1 with a remainder of 1
- Divide the quotient (1) by 2:
- 1 ÷ 2 = 0 with a remainder of 1
Now, collect the remainders from bottom to top (the last remainder to the first).
Reading the remainders upwards: 1100.
Therefore, the decimal number 12 is 1100 in binary.
Binary Representation Table
To further illustrate, here's a short table showing decimal numbers and their corresponding binary forms:
| Decimal Number | Binary Number |
|---|---|
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
Why Binary Matters
Binary is crucial because it aligns perfectly with the fundamental operation of digital electronics. Computers use transistors that are either "on" or "off," representing the two states of a binary digit (bit). A 1 signifies an "on" state or true, while a 0 signifies an "off" state or false. This simplicity allows for robust and efficient processing of information. Understanding how numbers like 12 are represented in binary is a foundational step in comprehending how computers store and process data. For more detailed information on number systems, you can explore resources like Decimal to Binary Conversion.
