Computer Science - Logic Gates
XOR gate notation + explanation
(A.B(line over B))+(A(line over A).B) As the notation means 'it's on if...' (e.g with AND it's on if A.B (A AND B are on) this notation means it's on if.. if A is the same and B is opposite (NOT) OR if B is the same and A is opposite (NOT) . This is proven by the truth table e.g Z is ON if A = 0 And B = 1 Because A is the opposite (0→1) and B is the same (1→1) BUT Z is not ON if A = 0 and B = 0 because there has been no change in either which does not fulfil the notation so it's not on!
NAND construction of an XOR gate + explanation (?)
1. A goes into a single input NAND gate (C ) and a double input NAND gate with D ( F ) 2. B goes into a single split input NAND gate (D) and a double input NAND gate with C (E) 3. E goes into a double input NAND gate with F
How to make circuits from statements
1. Circle the OR/AND commands in the stament e.g the statement IF (A OR B are ON) OR (B is ON) then system is ON 2. Put in your circuit the inputs stated in the stamens 3. Put in your circuit the respective logic gates for the commands in the statment e.g In the statment it says 'IF (A OR B are ON)' → the command is OR for A/B so in your circuit plug A and B into an OR gate 4. If the statement says 'IF A/B... is OFF' then you need a NOT gate because this checks for OFF (don't need one for ON it is automatically on??) - so if it says at the end 'then the system is off' put a NOT at the end (you can check this with the trace table) 5. ALWAYS do a truth table to check your answers it will automatically tell you if its wrong or righty * remember to do the statements in order with the inside brackets coming FIRST → if the statement is 'IF (A is OFF) OR (A and B are ON) do the 'A if OFF' first by plugging A into a NOT gate then do the ' A AND B are ON' by plugging them into an AND gate then do the OR outside the brackets by plugging the two products of the brackets into an OR. *if the truth table is the opposite of what you have put a NOT gate at the end to turn it all around
Logic circuit output steps:
1. Label the input and output gates (A,B...) 2.Draw the truth table with the appropriate columns 3. Explain the columns (Do the notation of the column to make calculation easier) 4. Calculate the output of the gates in order 5. Review the output and check
OR gate notation
A + B ( + symbolises OR)
Single split input truth table
A = 0,1 then Z = ?,?
Three input combination:
A = 00001111 B = 00110011 C= 01010101 (remember EIGHT and they all START ON ZERO and END ON ONE)
XOR gate truth table
A = 0011 B = 0101 Z = 0110
AND gate truth table
A = 0011 B = 0101 Z= 0001
NAND truth table
A = 0011 B = 0101 Z= 1110
NOR truth table
A = 0011 B=0101 Z= 1000
NOT gate truth table
A = 01 Z = 10 (opposite)
NAND construction of a NOT gate + explanation
A single split input NAND gate (NAND = When both inputs are on it's off → Single split input means the input is either 1,1 or 0,0 (the 1 or 0 is duplicated to fit the two inputs of the logic gate) so it automatically changes that input to the oposite if it's 1,1 = 0 (off) or if it's 0,0 = 1 (on))
NOT gate notation
A with a line over the top (The line symbolises NOT (the opposite) meaning that the output is NOT what A is (the opposite))
NOR gate notation
A+B with a line over the top (+ symbolises OR the line symbolises NOT = NOR)
AND gate notation
A.B ( The dot symbolises AND)
NAND gate notation
A.B with a line over the top (. symbolises AND, The line symbolises NOT = NAND)
Every or section show a capsule or a segment of the statement
AND links things so even if its out of order and should come before the 'final' or
What are NOR gates used by?
EEPROM (solid state memory)
What are NAND gates used by?
Flash memory (solid state memory)
OR gate description
If any input is ON, then its ON (A OR B are on then it's on vs for AND its when A AND B are on)
AND gate description
If both inputs (A & B) are ON then it is ON
XOR gate description
If the two inputs are the same, it's OFF
What is single split input:
It has ONE input that splits into two (two fit the logic gates), this makes the truth tables very simple - the input is just A = 0,1 and (for example) NOR is just Z = 1,0 because NOR is when either is ON it's OFF but as both inputs are A it tuns into if A is on then it's off
NAND gate description
It is the OPPOSITE of AND (NAND = NOT + AND) (NOT = The opposite). When both inputs are ON it's OFF
NOR gate description
It is the opposite of OR (NOR = NOT + AND) ( NOT = the opposite). If anything is on, it's off
NAND construction of an OR gate
Its all in the notation
How to make a purely NAND circuit from a circuit
Learn how to make the different logic gates in NAND then just convert each logic gate into its respective NAND parts a piece together correctley
NOT gate symbol
One line - Triangle pointing to the right with a circle on the end
XOR gate symbol
The OR symbol but with a line before the or symbol
Single split input notation
The same as normal logic gates but all inputs are labelled A e.g OR = A+A
Single split input symbol
The same gates just with either A,A as the input labels or one single input (A) split into two lanes
NAND construction of an AND gate + explanation
Two input NAND gate (1) going into a single input NAND gate (2) ( 1= NAND 2 = NOT → NAND + NOT = AND)
OR gate symbol
Two lines - Semi circle with a curved edge
AND gate symbol
Two lines - Semi circle with straight side on the left
NOR gate symbol
Two lines - semi circle with a curve instead of straight edge and a dot on the end (dot on symbol symbolises NOT)
NAND gate symbol
Two lines - semi circle with a dot at the end (dot on symbol symbolises NOT)
NAND construction of an OR gate + expliantion (?)
Two single input NAND gates going into a double input NAND gate
NAND construction of an NOR gate + explanation
Two single input NAND gates going into a double input NAND gate (1) then a single input NAND gate (2) (1 = OR 2 = NOT → OR + NOT = NOR)
NOT gate description
Z (output) is the inverse of A (input). Z is NOT A (opposite)
