DATA REPRESENTATION IN COMPUTER MEMORY

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

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

 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

 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

 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 Truth Table

 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

ABY Truth Table

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

 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

ABY Truth Table

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’

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

 Gates NOR  Gates NAND  Gates Exclusive –OR  Gates Exclusive –NOR

 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

InputOutput ABY

 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

INPUTOUTPUT ABY

 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

INPUTOUTPUT ABY

 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

INPUTOUTPUT ABY

 THANK YOU  TO BE CONTINUED….