How do you represent -123 in twos complement in 10 bit registers?

To represent -123 in two's complement using a 10-bit register, first represent the positive value 123 in binary, which is 01111011. Next, extend it to 10 bits: 001110110. Then, invert the bits to get 110001001. Finally, add 1 to this result: 110001001 + 1 = 110001010. Thus, -123 in two's complement using a 10-bit register is 110001010.