Convert ${\left(128\right)}_{10}$  into binary system.

To convert the decimal number 128 in binary, we follow the process of dividing the number by 2 and recording the remainders. Let's break it down step by step.

Step-by-Step Conversion of 128 to Binary

Start by dividing 128 by 2:

• 128 ÷ 2 = 64, remainder = 0
• 64 ÷ 2 = 32, remainder = 0
• 32 ÷ 2 = 16, remainder = 0
• 16 ÷ 2 = 8, remainder = 0
• 8 ÷ 2 = 4, remainder = 0
• 4 ÷ 2 = 2, remainder = 0
• 2 ÷ 2 = 1, remainder = 0
• 1 ÷ 2 = 0, remainder = 1

Now, write the remainders in reverse order: 10000000. This is the binary representation of the decimal number 128 in binary.

Final Answer

Therefore, 128 in binary is:

        (128)10 = (10000000)2

The binary representation of 128 is 10000000, which means that the number 128 is written as a series of 1's and 0's in the binary system.