Answer:
-8
Step-by-step explanation:
To represent -15 as a 6-bit two's complement binary number, follow these steps:
1. Start with the binary representation of the positive equivalent of the number (15 in this case), which is 000111.
2. Invert all the bits (change 0s to 1s and 1s to 0s) to get the one's complement: 111000.
3. Add 1 to the one's complement to get the two's complement: 111001.
Therefore, the 6-bit two's complement binary representation of -15 is 111001.
To find the decimal equivalent of the two's complement number 111000:
1. Check the most significant bit (MSB), which is the leftmost bit. If it is 1, it indicates a negative number.
2. Since the MSB is 1, the number is negative. In two's complement, to find the decimal equivalent, invert all the bits and add 1.
3. Inverting all the bits of 111000 gives 000111.
4. Adding 1 to 000111 gives 001000.
Therefore, the decimal equivalent of the two's complement number 111000 is -8.