1. Binary Addition & Subtraction

2. Addition Rules 0 + 0 = 00 ( 0 with a 0 carry )

3. Addition Rules
+ 0 1
+ 0
+ 1 1
+ 1
0 0
0 1
0 1
1 0

4. Addition Rules w/Carries
0+0+0 = 00 (0 WITH 0 CARRY)
0+0+1 = 01 (1 WITH 0 CARRY)
0+1+1 = 10 (0 WITH 1 CARRY)
1+1+1 = 11 (1 WITH 1 CARRY)

5. Adding Binary Numbers 1 1 1
10100
+11110 20
+30 1 50

6. Subtraction Rules

7. 1’S Complement
Invert all bits.
100011

8. 2’S Complement Invert all bits and then add one. 1) 10111011001) 2) 3)

9. 2’S Complement Quick Method
Example:
1) Start at the LSB and write down all zeros moving
to the left.
2) Write down the first “1” you come to.
3) Invert the rest of the bits moving to the left. 1 1 1

10. Subtract Positives w/Positive Answer
2’S complement the bottom number then add.
1001
+1011
1001 9
-0101 -5
Sign bit: One means positive, zero means negative.
1]0100 4

11. Subtract Positives w/Negative Answer
2’S complement the bottom number then add.
0101
+0111
0101 5
-1001 -9 -0 1
0]1100 -4
When the sign bit is negative, 2’s complement
your answer to find the magnitude of the number.

12. Subtracting Negatives
1) Convert the decimal numbers to binary.
2) Find the negative binary numbers.
3) 2’s complement of the bottom number, then add. -2
- -3 1
0010
-1101
1110
1110
+0011
0011
1]0001