Signed and Unsigned Integer Addition/Subtraction, please show steps so to clarif

Question

Signed and Unsigned Integer Addition/Subtraction, please show steps so to clarify.

Perform 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 c_0 to c_n (or b_0 to b_n). For the addition, determine whether there is an overflow. For the subtraction, determine whether we need to keep borrowing from a higher bit. 324 + 127 29 - 156 96 + 178 243 - 135 501 + 34 131 - 199 We need to perform the following operations, where numbers are represented in 2's complement: -29 + 156 -35 + 65 341 + 255 -256 - 220 128 - 129 -131 + 199 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: Using c_n, c_n-1 (carries). 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?

Explanation / Answer

a)

1)324+127

2) 96+178

3) 501+34

4) 29-156

5) 243-135

6) 131-199

b) by using 2's compliment

1) -29 + 156

-29= 00011101

invert bits = 11100010

add 1 = 11100011

2) 341+255

3) 128-129

-129=10000001

1's compilment = 01111110

add 1= 01111111

4) -35+65

-35=00100011

1's compliment=11011100

add 1=11011101

5) -256-220

6) -131+199

carry 0 1 1 1 1 1 0 0 0 324 1 0 1 0 0 0 1 0 0 127 0 0 1 1 1 1 1 1 1 addition 1 1 1 0 0 0 0 1 1

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