104 Flashcards
What values can boolean algebra take?
1 or 0
What is boolean addition?
> OR
Sum = 1 when any of the literals are 1
Sum = 0 when all the literals are 0
What is boolean multiplication?
> AND
Product = 1 when all literals are 1
Product = 0 when any literals are 0
What are the zero and unit rules?
> A.0 = 0
A.1 = A
A+1 = 1
A+0 = A
What are the complement relations?
> A.A ̅=0
A+A ̅=1
A= =A [double complemented A = A]
What are the Idempotence rules?
> A.A = A
> A+A = A
What are the communtative laws?
> A+B=B+A
> A.B = B.A
What are the absorption rules?
> A + A.B = A
A.(A+B) = A
A+ A ̅.B=A+B
What are the distributive laws?
> A.(B + C) = A.B + A.C
> A + B.C = (A + B).(A + C)
What are the associative laws?
> A + B + C = (A + B) + C = A + (B + C)
> A.B.C = (A.B).C = A.(B.C)
What are De Morgan’s Theorems?
> (A+B) ̅= A ̅.B ̅
> (A.B) ̅= A ̅+ B ̅
What is the rule of De Morgan’s Theorems?
Break the line and change the sign
What is a multi-input gate?
Instead of writing out several gates in a row, we often have a gate with multiple inputs.
What are the two De Morgan’s theorems in words?
> The complement of a product of variable is equal to the sum of the complemented variables.
The compliment of a sum of variables is equal to the product of the complemented variables
What is circuit minimisation?
This is the way of simplifying expressions to minimise operations
Why are NAND gates special?
All other primitive logic gates can me made from NAND gates
How can a NOT gate be made from NAND gates?
The input is the same for both inputs of the NAND gate
How can a AND gate be made from NAND gates?
A NAND gate where the output goes into both inputs of another NAND gate
How can a OR gate be made from NAND gates?
> y=(a ̅.b ̅ ) ̅
> Each input goes into both inputs of separate NAND gates. Each output of each NAND gate goes into another NAND gate
How can a NOR gate be made from NAND gates?
> Each input goes into both inputs of separate NAND gates. Each output of each NAND gate goes into another NAND gate. The output of this gate goes into both inputs of another NAND gate
Look in Notes to see what it looks like
How can an XOR gate be made from NAND gates?
> See notes
What does CMOS Stand for?
Complementary Metal-oxide semiconductor
What is CMOS?
> A technology used to make MOSFETS
> Made using semiconductors
What type of semiconductor is used in CMOS technology and what has happened to it?
> n-type: Electrons are added to make them more negatively charge
p-type: Holes are added to make it more positively charged
What are the two types of MOSFETS made from CMOS?
> n-channel MOSFETs (n-FET)
> p-channel MOSFETs (p-FET)
What happens when n-type and p-type silicone is put together?
> A region between them called the depletion region is formed
This region is nonconductive
What happens in a n-fet?
> When a positive charge is applied to the gate, it attracts electrons and causes the depletion region to conduct electricity and join the source and drain together
What happens in a p-fet?
When a negative charge is applied to gate, it attracts holes and causes the depletion region to conduct electricity and join the source and drain together
What is the structure of n-fet?
The negative silicone is on the top and the positive silicone is on the bottom
What is the structure of a p-fet?
The positive silicone is on the top and the positive silicone is on the bottom
How are gates made?
Using different transistors in different combinations
How are NOT gates made from transistors?
> The input is connected to 2 transistors in parallel, one p-type (source connected to Vdd) and one n-type (source connected to Vss)
The drain of both resistors are connected to the output
What is the difference between Vdd and Vss?
Vdd is positive (1) and Vss is negative (0)
How are NAND gates made from transistors?
> See Notes
What can be said about power efficiency of CMOS?
> There is no direct path between Vdd and Vss when transistors are static
This reduces power consumption
Power can pass between the two when the transistors switch
PRACTIVE KARNAUGH MAPS
DO IT
What is gray code?
> This is where only a single bit in a bit pair changes at a time
00 => 01 => 11 => 10
