Converting 119 to Binary: A Step-by-Step Guide
Have you ever wondered how to convert a decimal number like 119 into its binary equivalent? Binary, or base-2, is a system that uses only two digits, 0 and 1, to represent numbers. This is the language computers understand! While it might seem daunting at first, converting decimal numbers to binary is actually quite straightforward. Let's break it down step-by-step.
Understanding Binary
Before we dive into the conversion process, let's refresh our understanding of binary. In decimal, each digit's place value is a power of 10. For example, in the number 123, the '1' represents 100, the '2' represents 20, and the '3' represents 3.
In binary, each digit's place value is a power of 2. So, in the binary number 1011:
- The rightmost '1' represents 2⁰ (which is 1)
- The next '1' represents 2¹ (which is 2)
- The '0' represents 2² (which is 4)
- The leftmost '1' represents 2³ (which is 8)
Therefore, the binary number 1011 is equivalent to 8 + 4 + 1 = 13 in decimal.
Converting 119 to Binary
Now, let's convert 119 to binary using the repeated division method:
- Divide 119 by 2: 119 / 2 = 59 (remainder 1). We write down the remainder '1'.
- Divide the quotient (59) by 2: 59 / 2 = 29 (remainder 1). We write down the remainder '1'.
- Continue dividing the quotient by 2:
- 29 / 2 = 14 (remainder 1)
- 14 / 2 = 7 (remainder 0)
- 7 / 2 = 3 (remainder 1)
- 3 / 2 = 1 (remainder 1)
- 1 / 2 = 0 (remainder 1)
- Read the remainders from bottom to top: This gives us the binary equivalent of 119: 1110111.
Let's verify this result:
- 1110111 = (1 * 2⁶) + (1 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (1 * 2¹) + (1 * 2⁰) = 64 + 32 + 16 + 4 + 2 + 1 = 119
Conclusion
Converting decimal numbers to binary involves repeated division by 2 and keeping track of the remainders. This process might seem complex at first, but with practice, it becomes second nature. Understanding binary is crucial for anyone working with computers, as it's the fundamental language they use for processing information.