please show as much work as possible!

PROBLEM 1 (38 PTS) a) Perform the following additions and subtractions of the following unsigned integers. Use the fewest number of bits n to represent both operators. Indicate every carry (or borrow) from co to cn (or bo to bn). For the addition, determine whether there is an overflow. For the subtraction, determine whether we need to keep borrowing from a higher bit. (8 pts) Example (n=8): 54 + 210 0=) Ci=0 77 - 194 Borrow out! Cg=1 PO C=1 PO C=1 OP C5=1 oo Cz=1 OP C2=1 0= oo bg=1 Po b=0 0=q Ha b=0 oo b=0 oo b=0 O bg=0 Obz=1 Obo=0 54 = 0x36 210 = OxD2 0 0 1 1 0 1 1 0 + 1 1 0 1 0 0 1 0 77 = 0x4D = 194 = OxC2 0 1 0 0 1 1 0 1 - 1 1 0 0 0 0 1 0 Overflow! 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 23 + 403 103 + 204 128 - ) 199 - 107 225 + 31 137 + 886 b) We need to perform the following operations, where numbers are represented in 2's complement: (24 pts) -61 + 128 -126 + 263 -511 - 167 256 - 257 For each case: Determine the minimum number of bits required to represent both summands. You might need to sign-extend one of the summands, since for proper summation, both summands must have the same number of bits. Perform the binary addition in 2's complement arithmetic. The result must have the same number of bits as the summands. Determine whether there is overflow by: i. Using Cn Cn-1 (carries). ii. Performing the operation in the decimal system and checking whether the result is within the allowed range for n bits, where n is the minimum number of bits for the summands. If we want to avoid overflow, what is the minimum number of bits required to represent both the summands and the result? c) Perform the multiplication of the following numbers that are represented in 2's complement arithmetic with 4 bits. (6 pts) 0101x0111, 0101x1001, 1100x1010