The decimal number -380 can be represented as 010000100 in 2's complement form. This form is commonly used in computer systems to represent negative numbers. It allows for easy addition and subtraction of both positive and negative numbers using simple bitwise operations.
To represent the decimal number -380 in 2's complement form, follow these steps:
1. Convert the positive equivalent of the decimal number to binary. The positive equivalent of -380 is 380.
- Divide 380 by 2 repeatedly, noting the remainder at each step: 380 ÷ 2 = 190 with a remainder of 0; 190 ÷ 2 = 95 with a remainder of 0; 95 ÷ 2 = 47 with a remainder of 1; 47 ÷ 2 = 23 with a remainder of 1; 23 ÷ 2 = 11 with a remainder of 1; 11 ÷ 2 = 5 with a remainder of 1; 5 ÷ 2 = 2 with a remainder of 1; 2 ÷ 2 = 1 with a remainder of 0; 1 ÷ 2 = 0 with a remainder of 1.
- The binary representation of 380 is 101111100.
2. Invert the bits (change 0s to 1s and 1s to 0s) in the binary representation obtained in step 1.
- Inverting the bits of 101111100, we get 010000011.
3. Add 1 to the inverted binary representation obtained in step 2.
- Adding 1 to 010000011, we get 010000100.
4. The resulting binary representation, 010000100, represents -380 in 2's complement form.
To summarize, the decimal number -380 can be represented as 010000100 in 2's complement form. This form is commonly used in computer systems to represent negative numbers. It allows for easy addition and subtraction of both positive and negative numbers using simple bitwise operations.