Perform the arithmetic addition of the two decimal numbers given in List-I using the signed-complement system. Match the corresponding output of List-I with binary number representation given in List-II. $$ \begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A)~ +6, +13 & (I)~ 00000111 \\ \hline (B)~ -6, +13 & (II)~ 00010011 \\ \hline (C)~ +6, -13 & (III)~ 11101101 \\ \hline (D)~ -6, -13 & (IV)~ 11111001 \\ \hline \end{array} $$
Step-by-step Solution:
Binary Conversions (8-bit signed 2's complement): +6 = 00000110 +13 = 00001101 -6 = 11111010 -13 = 11110011 Calculations: (A) +6 and +13 00000110 + 00001101 = 00010011 Matches (II) (B) -6 and +13 11111010 + 00001101 = 100000111 Discard carry 1 -> 00000111 Matches (I) (C) +6 and -13 00000110 + 11110011 = 11111001 Matches (IV) (D) -6 and -13 11111010 + 11110011 = 111101101 Discard carry 1 -> 11101101 Matches (III) Correct Code: (A)-(II), (B)-(I), (C)-(IV), (D)-(III)