Lecture 5: Combinational Logic 2

Complement = variable with a bar over it

Literal = variable or its complement

Implicant = product of literal == (AB) , (ABC) ...

Minterm = product (AND) taht includes all input variables == (ABC) , (A`BC) ...

 

Sum of Products Form (SOP)

First make truth table to Canonical From , than optimize it using axioms or other boolean expression tool.

 

Product of Sums (POS) = Demorgan of SOP

 

 

Building larger block like decoder, mutiplexer to abstract and hide logic gate.

 

Decoder

n inputs and 2^n outputs

 those As could be the address of row in DRAM or instruction in the program (opcode) and we use decoder to get what that bit pattern tells us.

 

Multiplexer , Selector

Selects one of the N inputs to connect it to the input 

we have 2 input , 1 select , 1 output

 

Full Adder

Binary addition

handling just single bit we can use this as module and implement n bits adder.

power of abstraction.

 

Programmable Logic Array (PLA)

we can see that first and gate and or gate is not used

{AND , OR , NOT} is logically complete. also {NAND} , {NOR} gate is complete by itself.

 

Tri State Buffer

E stands for Enable. Z means floating value , it doesn't mean it is wrong value it means output is not driven by certain input in this case A.

needed when we control CPU and memory.