Boolean algebra (unit 8) (Finished) Flashcards
(8.1) What are computers made of?
billions of switches that can be on or off
(8.1) How can switches in computers be used together
to create a logic gates
(8.1) What is a logic gate
Gates that take one or more inputs and output a single output
(8.1) What are the 4 main types of logic gates?
NOT
AND
OR
XOR
(8.1) What is a NOT gate
If 0 is input it outputs 1
If 1 is input it outputs 0
Triangle + ball shape
(8.1) What is an AND gate?
Both inputs have to be 1 in order to make the output 1
Otherwise the output is 0
fat semicircle shape
(8.1) What is an OR gate?
If either of the inputs are 1 then the output is 1
if both are 0 then the output is 0
Fat arrow shape
(8.1) What is an XOR gate?
exclusive or, means that only 1 of the inputs can be positive to make a positive output
Fat arrow with underlining shape
(8.1) What is a logic circuit?
The combination of multiple logic gates to create a circuit
(8.1) What is the symbol for a NOT gate?
dog leg (¬)
(8.1) What is the symbol for a AND gate?
up arrow (∧)
(8.1) What is the symbol for a OR gate?
V (∨)
(8.1) What is the symbol for a XOR gate?
Underlined V (⊻)
(8.1) How else can logic circuits be displayed?
Through Boolean expressions using symbols for the logic gates
(8.1) What is De Morgan’s first law?
¬(A ∨ B) = ¬A ∧ ¬B
NOT (A OR B) = NOT A AND NOT B
(8.1) What is De Morgan’s second law?
¬(A∧B) = ¬A∨¬B
NOT(A AND B) = NOT A OR NOT B
(8.2) How can logic circuits be broken down into expressions
By finding the expression for each logic gate, then combining them at the end
(8.2 is basically all expansion on 8.1 and mostly practice Boolean questions)
(8.3) What is a karnaugh map?
an alternative, easier method of displaying expressions in comparison to truth tables
(8.3) How are karnaugh maps structured?
One value takes the X axis, one takes the Y axis
(8.3) What happens if there are 3 variables in a karnaugh map?
Two of the variables go along the same side, going 00 01 11 10 instead of just 1 or 0
(8.3) What happens if there are 4 variables in a karnaugh map?
There are now two variables on both axis of the map, each having 00 01 11 10
(8.4)What is a half-adder?
A circuit that performs the addition of two bits
has the s column for the result and the c column for the carry bit
(8.4)What is the formula for column C in a half adder?
C = A ∧ B
(8.4)What is the formula for column S in a half adder?
S = A ⊻ B
(8.4)What are the limitations of a half adder?
Can only add 1 bit numbers
it cannot use the carry from a previous addition as a third input to a subsequent addition
(8.4)What is a full adder?
Combines 2 half adders into one, allows for more complex calculations
(8.4)How many inputs does a full adder have?
3
(8.4)Can multiple full adders be connected together?
Yes
(8.4)What is a flip flop?
an elemental sequential logic unit
(8.4)What is a D-type flip flop?
Has a data input (D) and a clock signal output
Can store 1 bit
(8.4)How does edge triggering work with D-type flip flops?
If D is the same on the next clock pulse, the flip flop will retain its current value, otherwise it will flip
(8.4)What are the uses of D-type flip flops?
Multiple D-type flip-flops are used to create registers and counters inside the CPU
They are used for the intermediate storage needed during arithmetic operations
Static RAM is also created using D-type flip-flops
