Final answer:
The question involves subtracting two's complement binary numbers and converting the final binary answer to decimal. The subtraction is performed by taking two's complement of the numbers being subtracted and adding them up. The result's sign is determined by its most significant bit, and the final decimal value reflects this.
Step-by-step explanation:
The question involves performing subtraction using two's complement binary representation and converting the results to decimal. The operation given is: 0000 1111 1111 1100 - 0101 0000 - 1111 0001. To subtract binary numbers, we invert the digits of the number to be subtracted (take two's complement) and then perform binary addition. Here are the steps to solve the problem:
- Take the two's complement of 0101 0000 to get 1010 1111.
- Add this to 0000 1111 1111 1100.
- Take the two's complement of 1111 0001 to get 0000 1111.
- Add this result to the sum from step 2.
Next, convert the binary result to decimal.
Remember that in two's complement, if the leftmost bit (most significant bit) is a 1, the number is negative in decimal form. If the bit is 0, the number is positive. Therefore, the sign of the final decimal result will depend on the most significant bit of the binary result.
Let's consider the rules for adding and subtracting numbers with different signs:
- When two positive numbers add, the answer has a +ve sign, e.g., 3+2 = 5.
- When two negative numbers add, the answer has a -ve sign, e.g., -4 + (-2) = -6.
- When two numbers having opposite signs add, subtract the smaller number from the larger number, and the answer has the sign of the larger number. For example, -5 +3 = -2.