Question

(1) For the following byte addition operations, list the result of addition, and what happens to the three status flags, Z (zero), N (negative), and V (overflow). Assume we're dealing with signed bytes. (10 pts. each) (1.1) 10010110 + 01101001 (1.2) 10110100 + 10010101

Answer 1

Answer:
--------
1)
Z = 0
N = 1
V = 0

2)
Z = 0
N = 0
V = 1

Explanation:
-------------
1)
Adding 10010110 and 01101001 in binary
    10010110
    01101001
-------------
 (0)11111111
-------------
Sum does not produces a carry
So, sum of these numbers in binary is 11111111

Verification
---------------
first = 10010110
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   10010110 is flipped to 01101001
II. Add 1 to above result
01101001 + 1 = 01101010
III. Now convert this result to decimal value
Converting 1101010 to decimal
1101010
=> 1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+1x2^1+0x2^0
=> 1x64+1x32+0x16+1x8+0x4+1x2+0x1
=> 64+32+0+8+0+2+0
=> 106
Answer: -106

second = 01101001
since left most bit is 0, this number is positive
so, we can directly convert this into a decimal value
Converting 1101001 to decimal
1101001
=> 1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
=> 1x64+1x32+0x16+1x8+0x4+0x2+1x1
=> 64+32+0+8+0+0+1
=> 105
Answer: 105

sum = 11111111
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   11111111 is flipped to 00000000
II. Add 1 to above result
00000000 + 1 = 00000001
III. Now convert this result to decimal value
Converting 1 to decimal
1
=> 1x2^0
=> 1x1
=> 1
=> 1
Answer: -1
This is correct since we can verify that -106+105 = -1
So, there was no overflow.

2)
Adding 10110100 and 10010101 in binary
    10110100
    10010101
-------------
 (1)01001001
-------------
Sum produces a carry of 1. We can ignore that carry.
So, sum of these numbers in binary is 01001001

Verification
---------------
first = 10110100
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   10110100 is flipped to 01001011
II. Add 1 to above result
01001011 + 1 = 01001100
III. Now convert this result to decimal value
Converting 1001100 to decimal
1001100
=> 1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x64+0x32+0x16+1x8+1x4+0x2+0x1
=> 64+0+0+8+4+0+0
=> 76
Answer: -76

second = 10010101
since left most bit is 1, this number is negative number.
so, follow these steps below to convert this into a decimal value.
I. first flip all the bits. Flip all 0's to 1 and all 1's to 0.
   10010101 is flipped to 01101010
II. Add 1 to above result
01101010 + 1 = 01101011
III. Now convert this result to decimal value
Converting 1101011 to decimal
1101011
=> 1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+1x2^1+1x2^0
=> 1x64+1x32+0x16+1x8+0x4+1x2+1x1
=> 64+32+0+8+0+2+1
=> 107
Answer: -107

sum = 01001001
since left most bit is 0, this number is positive
so, we can directly convert this into a decimal value
Converting 1001001 to decimal
1001001
=> 1x2^6+0x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
=> 1x64+0x32+0x16+1x8+0x4+0x2+1x1
=> 64+0+0+8+0+0+1
=> 73
Answer: 73
-76+-107 must be -183
This is not correct since we can verify that -76+-107 not equals 73
So, there was an overflow.