Flashcards
19: Logic Circuits and Boolean Algebra
Cards in this deck (36)
- 1What does chapter introduce?Chapter introduces some specific circuits that are used to construct components that provide functionality in computer hardware.
- 2What is the simplest circuit that can be used for binar addition?Half adder
- 3describe a diagram of a half adderCircuit takes 2 input bits and ouputs a sum bit and a carry bit
a - - S
1 bit half adder circuitry
b- - C - 4Give the truth table for a half adder
- 5Half Adder CircuitA circuit which performs binary addition of two individual bits
- 6What would a possible circuit be for half adder based on truth table?an AND symbol for C output. For S ouput can math XOR operator. One ciruit produce half addre functionality contain an AND gate and an XOR gate with each receiving input from A and B. Other ways ie with just NAND gates
- 7Full Adder CircuitA circuit which performs binary addition of two individual bits and an input carry bit.
- 8Describe the full adder circuit - when used?used if 2 numbers expressed in binary with several bits to be added, addition must start with 2 least sig bits and proceed to most sig bits. At each stage, carry from the previous addition has to be incorporated into current addition. If half adder used each time, has to be separate circuitry to handle the carry bit because half adder only takes 2 inputs. Full adder: has 3 inputs including previous carry bit.
- 9give the truth table for a full adder circuit
- 10Combinational CircuitA circuit in which the output is dependent only on the input values.
- 11Sequential CircuitA circuit in which the ouput depends on the input values and the previous output.
- 12SR Flip-flop or latch is what type of circuit?sequetial
- 13Describe SR flip-flop. Properties allow to?can be constructed with 2 NAND gates or 2 NOR gates. Self-consistend state referred as set state. Properties (next card) explain why SR flip=flop can be used as a storage device for 1 bit and could be used as a component in RAM as a value is sotred but can be altered.
- 14What are some interesting consequences with hypothetical situations of inputsie if R, S, Q, Q' all had value 0 is self-contradictory as 2 inputs values 0 to a NOR gate produce a 1 output. ie Q and Q' both set to 1 would be self-contradictory as ouput from a NOR gate is alwas 0 if either input it 1. Flip-flop is therefore a 2 state decice. Either it has Q=1 and q'=0 or reverse.
ie S and R = 1 as leads to invalid state with both Q and Q' = 0. Due to this the circuit must be protected from recdeiving an input signal on R and S simultaniously - 15Give truth table/ diagram of SR flip flop
- 16JK flip-flop describe - errors could happen and how tries to preventin addition to poss of entering an invalid state these is potential for a circuit to arrive in a uncertain state if inputs do not arrive quite at same time. In order to prevent this a circuit may incldue a clock pulse input to give better change oc synchronising inputs.
- 17What is the special case for the use of all NAND gates and the one for using all NOR gates?NAND - when all inputs are 1 output is 0
NOR - all inputs 0 output is 1 - 18What is the dif betweena JK flip-flop and SR flip-flopJK behaves similary as SR as a strorage device for one bit. However if both J and K are inputs as a 1 then the values for Q and Q' are toggled (switch value). Makes JK a more reliable device as no combination of input states that leave uncertainty as to which values are stored
- 19Give truth table/ diagram of JK flip flop
- 201+1 =? for denary arithmetic2
- 211+1 =? for binary arithmetic10
- 221+1 =? for bit arithmetic0
- 231+1 =? for Boolean algebra1
- 24Boolean algebra: 1 =? 0 =? + =?1 = True
0 = False
+ = OR - 25True or True is?True
- 26A AND B can be represented as?A.B
AB - 27NOT A =?-
A - 28Give the Boolean algebra identities (laws) Double complement = = A = A for both and form and or form
- 29how can interchange and and or forms?an identity wrriten in one form can be transformed into the other by intercchanging each 0 or 1 and each and or or
ie 0.A = A (False and A is False)
-
True or A is True 1+A=1 - 30go over simplifying boolean algebra*******
(GO OVER!) - 31how to create a boolean algebra expression directly from a truth tablefind onlyu rows of table creating a 1 output for C
*go over - 32The boolean algebra representation of a logic circuitGO OVER - DO PRACTICE QUESTIONS
What creates a 1 - 33What are Karnaugh maps (K-maps)?a method of creating a boolean algebra expression from a truth table. Makes easier
****Practice questions do****** - 34Describe k mapsonly cells containing 1 are considered
groups of cells containing 1s are identified ie row, colom or rectangle. contain 2, 4, 8...
If an individual cell cannot be contained in any group it is treated as being a group. Within each group only input values retained are those which retain a constant value throughout the group - 35What do with 3 or 4 inputs for k-mapsBC 00 01 11 10
A(D)
0(0)
1(0)
(11)
(10) - 36Describe the role of flip-flops in a computerA flip-flop can achieve a stable state and this state can be toggled by an appropriate input. This means
that it can act as a memory component storing a value for 1 bit.
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- A Level AL Computer Science (Advanced Theory) Flashcards on 19: Logic Circuits and Boolean Algebra, created by HRYN red on 17/01/2023.
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