1. Binary Addition Rules Adding Binary Numbers 0 + 1 = 1 1 + 0 = 1
0 + 0 = 0
1 + 1 = 0 (carry one)
carry = 1 (carry one)

2. Example 111111 1011011 +100111 --------------10000010 carries result
*** The last carry is placed at the left hand side

3. Let’s try this…
101000
110100
111100
111101

4. Let’s try this…
101011
110100
101111

5. Subtracting Binary Numbers
Binary Subtraction Rules
take the second value (the number to be subtracted) and apply TWO'S COMPLEMENT (change 1 for 0 and 0 for 1)
add 1 to the result (of two’s complement)
add the complemented value to the first value; during addition we disregard the last carry

6. Example

7. Let’s try this…
– 111
110111
110010
11010

8. Let’s try this…
– 101
101001
11011

9. Multiplying Binary Numbers
Binary multiplication can be achieved in a similar fashion to multiplying decimal values.
Multiply each digit using the standard method;
Add the results using the binary addition rules

10. Example
1011 x 111
Notice the pattern in the partial products, as you can see multiplying a binary value by two can be achieved by shifting the bits to the left and adding zeroes to the right.

11. Let’s try this…
11001 x 11
10011 x 101
x 110
11111 x 101
x 100

12. Seatwork:
x 111
x 1011
1000
11110

13. Dividing Binary Numbers
Binary division can be achieved in a similar fashion to dividing decimal values.
Divide the divisor from the dividend
Use the simple subtraction rules whenever necessary, as follows:
0 – 0 = 0
1 – 1 = 0
1 – 0 = 1
0 – 1 = 1 (with borrow)

14. Example
          11   r = 10  11 )1011          -11           101            -11             10  <-- remainder, R

15. Let’s try this…
100 / 10
111 / 11
1010 / 100
1101 / 11
10111 / 10 10
10 r 1
10 r 10
100 r 1
1011 r 1

16. Compute the ff.:
x 101
x 11
/ 111
/ 1010

17. Compute the ff.:
1010 r 11
r 100