Boolean Logic
Download as PPT, PDF1 like525 views
This document discusses Boolean logic and digital logic basics. It covers topics like logic gates (AND, OR, NOT), transistors, truth tables, precedence rules, NAND and NOR gates, integration levels from SSI to VLSI, logical expressions, equivalence, and Boolean algebra properties.
Boolean Logic
- 1. Boolean Logic Basics Combinational Circuits Sequential Circuits Inam Ul-Haq Senior Lecturer in Computer Science University of Education Okara Campus Inam.bth@gmail.com Member at IEEE & ACM Thanks to Adapted from the slides prepared by S. Dandamudi for the book, Fundamentals of Computer Organization and Design.
- 2. Introduction to Digital Logic Basics Hardware consists of a few simple building blocks These are called logic gates AND, OR, NOT, … NAND, NOR, XOR, … Logic gates are built using transistors NOT gate can be implemented by a single transistor AND gate requires 3 transistors Transistors are the fundamental devices Pentium consists of 3 million transistors Compaq Alpha consists of 9 million transistors Now we can build chips with more than 100 million transistors
- 3. Basic Concepts Simple gates AND OR NOT Functionality can be expressed by a truth table A truth table lists output for each possible input combination Precedence NOT > AND > OR F = A B + A B = (A (B)) + ((A) B)
- 4. Basic Concepts (cont.) Additional useful gates NAND NOR XOR NAND = AND + NOT NOR = OR + NOT XOR implements exclusive-OR function NAND and NOR gates require only 2 transistors AND and OR need 3 transistors!
- 5. Basic Concepts (cont.) Proving NOR gate is universal • Proving NAND gate is universal
- 6. Logic Chips (cont.) Integration levels SSI (small scale integration) Introduced in late 1960s 1-10 gates (previous examples) MSI (medium scale integration) Introduced in late 1960s 10-100 gates LSI (large scale integration) Introduced in early 1970s 100-10,000 gates VLSI (very large scale integration) Introduced in late 1970s More than 10,000 gates Explore how many transistors in SSI? Explore how many transistors in MSI? Explore how many transistors in LSI? Explore how many transistors in VLSI?
- 7. Logic Functions Logical functions can be expressed in several ways: Truth table Logical expressions Graphical form
- 8. Logic Functions (cont.) Truth Table A B C F 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Logical expression form F = A B + B C + A C Graphical Form
- 9. Logical Equivalence All three circuits implement F = A B function
- 10. Logical Equivalence Derivation of logical expression from a circuit(graphical form) Trace from the input to output Write down intermediate logical expressions along the path (write down truth table of expression F3)
- 11. Logical Equivalence (cont.) Proving logical equivalence: Truth table method (write down graphical form from below truth table) A B F1 = A B F3 = (A + B) (A + B) (A + B) 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1
- 12. Boolean Algebra (2nd method) (Prove each property through truth table)
- 13. Boolean Algebra (cont.) (Prove each property through truth table)