Mohammad Amin Kuhail M.Sc. (York, UK) University of Palestine Faculty of Engineering and Urban planning Software Engineering Department Digital Logic Design.

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Presentation transcript:

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

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

Binary operations Addition Subtraction Multiplication Division Agenda

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

Complements Example: Find the 9’s complement for: Definition

Complements Example: Find the 9’s complement for: Definition

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

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

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

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

Arithmetic Addition and Subtraction Careful: overflow Examples:

Binary codes Definition, Examples

Binary codes BCD Excess 3 Other Binary Codes

Binary codes Addition

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