As we know 2's complement of a number vary from
(n-1) ) to 2(n-1) - 1
43 is between -64 to 63, so n= 7. Therefore minimum 7 bits is needed.
In 2's complement representation, for positive number the number can be written as 0 followed by its binary representation.
for negative number 1 followed by 2's complement of it's binary representation.
As 43 is a positive number so 0 followed by binary representation of 43
43 = 32+8+2+1 = 0101011
But options are in 8 bit representation so we can make 7bit number to 8bit by sign extension in 2's complement representation i.e if first bit is 1 the new leftmost bit will be 1 and if it is zero then new leftmost bit will be 0.
so we can rewrite 43 as 00101011 which is option C.