# Arithmetic Overflow

1. Feb 5, 2008

### needhelp83

Perform the following operations, representing the decimal numbers in 8-bit two’s complement code. Analyze whether the operations produce arithmetic overflow. Explain how you have estimated the overflows.

20 – 5; 127 –126; 127 – 128; -20 – 111; -20 – (+111);
- 43 - 120; -127 – 2; - 126 – 2.

I am having a very difficult time trying to understand this overflow concept. Any guidance would be greatly appreciated

*20-5
0001 0100 (20)
1111 0100 (-5) 2's

1 0000 1011

No overflow

*127-126
0111 1111 (127)
1000 0010 (-126) 2's

1 0000 0001 No overflow

*127 - 128
0111 1111 (127)
1000 0000 (-128) 2's

1111 1111 No overflow or carryout

*-20-111
1110 1100 (-20) 2's
1001 0001 (-111) 2's

1 0111 1101 Overflow (adding two negatives gives a positive)

*-20 - (+111)
1110 1100 (-20) 2's
1001 0001 (-111) 2's

1 0111 1101 Overflow (adding two negatives gives a positive)

*-43-120
1101 0101 (-43) 2's
1000 1000 (-120) 2's

1 0101 1101 Overflow (Adding 2 negatives gives a positive)

*-127-2
1000 0001 (-127) 2's
1111 1110 (-2) 2's

1 0111 1111 (Overflow 2 negatives gives a positive)

*-126-2
1000 0010 (-126) 2's
1111 1110 (-2) 2's

1 1000 0000 (No overflow)

Am I doing this correctly?

2. Feb 6, 2008

Any help?

3. Feb 6, 2008

### mgb_phys

In twos complement you can represent a range -2^(n-1) to +2^(n-1) - 1
So in 8 bits you can fit numbers from -128 to 127
An interesting feature is that the most negative number is larger magnitude than the largest positive number.

4. Feb 6, 2008

### needhelp83

Have I shown this properly according to the instructions provided?