1. DATA REPRESENTATION IN COMPUTER MEMORY

2.  Describe the coding system:  Sign and magnitude  1’s Complement and 2’s Complement  Binary Coded Decimal (BCD system)  ASCII and EBCDIC Previous Lesson

3. By the end of topic, the students should know:  Perform operations with Boolean Algebra  Define logic gates.  Explain the operation of logic gates  Draw the logic symbols for the following logic gates : NOT, AND, OR, NOR, NAND, Exclusive –OR and Exclusive –NOR  Construct truth table of logic gates. LESSON LEARNING OUTCOME

4.  Digital (logic) circuits operate in the binary mode where each input and output voltage is either 0 or 1.  This characteristic of logic circuits allow us to use Boolean Algebra as a tool for the analysis and design of digital systems.  The input are considered logic variables whose logic levels at any time determine the output levels.  In our work to follow, we shall use letter symbols to represent logic variables. For example, the letter A might represent a certain digital circuit input or output, and any time we must have either A= 0 or A=1; if not one, then the other. Logic Gates

5.  In Boolean Algebra, there are only 3 basic operations : OR, AND, NOT (logic operations)  Digital circuits called logic gates can be constructed from diodes, transistors, and resistors connected in such a way that the circuit output is the result of a basic logic operation Logic Gates

6.  Can be performed on a single input variable  Example : if the variable A is subjected to the NOT operation, the result x can be expressed as Gates NOT X = A Presence of small circle always denotes inversion AY 01 10 Truth Table

7.  The AND gate output is equal to the AND product of the logic input, that is x=AB.  In other words, the AND gate is a circuit operates in such way that its output is HIGH only when all its input are HIGH. Gates AND

8. ABY 000 010 100 111 Truth Table

9. Summary of the AND operation  The AND operation is performed the same as ordinary multiplication of 1 and 0  An AND gate is logic circuit that performs the AND operation on the circuit’s inputs  An AND gate output will be 1 only for the case when all inputs are 1, for all other cases the output will be 0  The expression x=AB is read as ‘x equals A AND B’ Gates AND

10.  Circuit that has two or more inputs and whose output is equal to the OR combination of the inputs.  The OR gate operates in such a way that its output is HIGH (logic 1) if either input A and B or both are at logic 1 level. Gates OR

11. ABY 000 011 101 111 Truth Table

12. Gates OR Summary of the OR operation  The OR operation produces a result (ouput) of 1 whenever any input is a 1.Otherwise the output is 0.  An OR gate is logic circuit that performs an OR operation on the circuit’s inputs  The expression x = A+B is read as ‘x equals A or B’

13. ORANDNOT 0+0 = 00.0 = 00 = 1 0+1 = 10.1 = 01 = 0 1+0 = 11.0 = 0 1+1 = 11.1 = 1 Summary of Boolean Operations

14.  Gates NOR  Gates NAND  Gates Exclusive –OR  Gates Exclusive –NOR

15.  NOR gate is a combination of the OR gate and NOT gate.  It works as an inverted OR gate. It is the same as OR gate symbol except it has a small circle on the output.  This small circle represents inversion operations. This gate will give an inverted output of the OR gate. Gates NOR

16. InputOutput ABY 001 010 100 110

17.  NAND gate is a combination of AND gates and NOT gates.  Its function is to invert the output of AND gate. It is the same as AND gate symbol except for the small circle on the output.  Once again the circle marks the inverse operation.  Thus, the NAND gate operates as an AND gate followed by an inverter. Gates NAND

18. INPUTOUTPUT ABY 001 011 101 110

19.  Two special logic circuit that normally found in digital systems are circuit-Or and Exclusive Exclusive-Nor.  Get Exclusive-Or is a combination of the three basic gates gates NOT, AND and OR.  Get Exclusive-or also known as EX-OR. Gates EXCLUSIVE-OR

20. INPUTOUTPUT ABY 000 011 101 110

22.  Exclusive-Nor gate operations (summarized: EX-NOR) is operating contrary to the Exclusive-Or.  Symbol for EX-NOR obtained simply by adding a small circle at the output of the EX-OR symbols. Gates EXCLUSIVE-NOR

23. INPUTOUTPUT ABY 001 010 100 111

25.  THANK YOU  TO BE CONTINUED….