1. Mohammad Amin Kuhail M.Sc. (York, UK) University of Palestine Faculty of Engineering and Urban planning Software Engineering Department Digital Logic Design Saturday, 22 September 2007 Lecture 3 of Binary Systems, Part II

2. Binary operations Complements Signed Binary Numbers Binary Codes Binary Storage and Registers Binary Logic Agenda

3. Binary operations Addition Subtraction Multiplication Division Agenda

4. Complements Are used in digital computers for simplifying the subtraction operation and for logical manipulation Definition, the r’s complement

5. Complements Example: Find the 9’s complement for: 1.546700 2.012398 Definition

6. Complements Example: Find the 9’s complement for: 1.546700 2.012398 Definition

7. Signed Binary Numbers With positive numbers, the most left eighth bit is 0. With negative numbers, the most left eighth bit is 1. Positive, Negative signed numbers

8. Signed Binary Numbers Signed magnitude representation Signed 1’s complement representation Signed 2’s complement representation Ways to represent negative numbers

9. Signed Binary Numbers Example: -9 Example: -11 Signed magnitude representation

10. Signed Binary Numbers Example: -9 Example: -11 Signed 1magnitude representation

11. Arithmetic Addition and Subtraction Careful: overflow Examples:

12. Binary codes Definition, Examples

13. Binary codes BCD 8421 2421 Excess 3 Other Binary Codes

14. Binary codes Addition

15. Binary Logic Binary logic consists of variables and logical operations: AND, OR, NOT Definition