Final answer:
To convert a decimal number to 8-bit two's complement, positive numbers are converted to binary and zero-padded to 8 bits, while negative numbers are converted to binary, inverted, and then added with 1. All digits in the binary representation are significant and there's no concept of rounding as in decimal numbers.
Step-by-step explanation:
To convert decimal numbers to 8-bit two's complement, one must first understand that two's complement is a method of representing positive and negative integers in binary. It allows for simple addition operations between positive and negative numbers. The highest bit (leftmost) determines the sign, where 0 indicates a positive number and 1 indicates a negative number.
To convert a positive decimal number to an 8-bit two's complement:
- Convert the absolute value of the number to binary.
- Padd the binary number with zeros to make it 8 bits, if it is not already.
To convert a negative decimal number to an 8-bit two's complement:
- Convert the absolute value of the number to binary.
- Padd the binary number with zeros to make it 8 bits, if it is not already.
- Invert all the bits (1 becomes 0, and 0 becomes 1).
- Add 1 to the inverted number. This is the two's complement binary representation.
The specific reasoning provided by the student, which discusses rounding up numbers, appears to be related to decimal rounding rather than the binary conversion process. In two's complement conversion, all digits are significant, and there is no rounding; each bit has a specific value contributing to the overall number representation.