Binary Addition & Subtraction

1. Binary Addition & Subtraction

2. Addition Rules • 0 + 0 = 00 ( 0 with a 0 carry ) • 0 + 1 = 01 ( 1 with a 0 carry ) • 1 + 0 = 01 ( 1 with a 0 carry ) • 1 + 1 = 10 ( 0 with a 1 carry )

3. 0 + 0 1 + 0 0 + 1 1 + 1 Addition Rules 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. 1 1 0 0 1 1 0 0 1 0 Adding Binary Numbers 10100 +11110 20 +30 50

6. Subtraction Rules

7. 1’S Complement Invert all bits. 100011 0 1 1 1 0 0

8. 2’S Complement Invert all bits and then add one. 1) 1011101100 2) 0100010011 + 1 3) 0100010100

9. 2’S Complement Quick Method 1011101100 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. 0 1 0 0 0 1 0 1 0 0

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

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

12. 1110 1110 -2 - -3 -1101 +0011 1 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. 0010 0011 1]0001