1. Negatives, Addition, Subtraction
Binary
Negatives, Addition, Subtraction

2. Storing Negative Integers
Another method is 2s Complement
-75 64 32 16 8 4 2 1
128
-128 1 1 1 1 1
=-75

3. 2s Complement Conversion
-117
Stage 1 : work out 117 in binary
128 64 32 16 8 4 2 1
Stage 2 : Reverse the 0’s and 1’s
-128 64 32 16 8 4 2 1 1
Stage 3 : Plus 1

4. Binary Addition In binary these are the possible sums… 0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, carry 1
= 1, carry 1
= 0, carry 0, carry 1

5. Binary Addition Example 1
= 89
128 64 32 16 8 4 2 1
75=
14=
Carry 89 1 1 1 1 1 1 1

6. Binary Addition Example 2
= 136
128 64 32 16 8 4 2 1
79=
57=
Carry
136 1 1 1 1 1 1 1 1 1

7. Binary Addition Example 3
= 150
128 64 32 16 8 4 2 1
75=
Carry
150 1 1 1 1 1 1 1 1

8. Binary Addition Example 4
128 64 32 16 8 4 2 1 26
138 87
251
Carry 1 1 1 1 1 1 1 1 1 1 1

9. Binary Addition Example 5
128 64 32 16 8 4 2 1
109 39 45
Carry 1 1 1
193 1 1 1 1 1 1

10. Binary Addition Example 6
128 64 32 16 8 4 2 1
151 42 31
Carry 1 1 1
224 1 1 1 1 1 1

11. Binary Subtraction
CPUs can’t subtract, they can only add!
75-14=61
The same as…
75+(-14)=61
Positive + Negative = Negative
To do this we need 2s Complement
-128 64 32 16 8 4 2 1

12. Binary Subtraction Example 1
75-14=61
75+(-14)=61
-128 64 32 16 8 4 2 1
75=
-14= 61 1 1 1 1 1 1 1 1

13. Binary Subtraction Example 2
91-18=73
91+(-18)=73
-128 64 32 16 8 4 2 1
91=
-18= 73 1 1 1 1 1 1 1 1 1 1