[Semester 1] Combinational Logic

Question 1

Where might you find an adder?

Answer 1

In the Arithmetic Logic Unit (ALU); it’s used to add numbers together (hence the name!)

Question 2

Sum

Answer 2

The total of the numbers being added. It’s true if only one input is true.

Question 3

Carry

Answer 3

Anything that needs to be carried over during addition

Question 4

True or false: Carry is only true if all inputs are true

Answer 4

Both! This is true in a half adder but in a full adder, only one input (one of the AND gates) has to be true.

Question 5

Delay

Answer 5

How long a circuit takes to calculate an output

Question 6

Look Ahead Carry

Answer 6

Looks at lower bits to see whether a higher carry will be generated

Question 7

Why does the delay in a Ripple Carry adder increase with each adder?

Answer 7

An adder can’t calculate sum and carry until it receives the carry from the previous adder.

Question 8

Comparator

Answer 8

Compares two currents and uses the largest one

Question 9

Multiplexer (mux)

Answer 9

Selects an output based on what the majority of input signals are equal to

Question 10

Control signal

Answer 10

Decides which input signal to use for the circuit’s output

Question 11

True or false: The more input signals there are, the more control signals needed.

Answer 11

True! If a mux has 8 input signals for example, it will need 3 control signals in order to create 8 possible combinations.

Question 12

Encoder

Answer 12

Converts multiple input signals into a single output

Question 13

Decoder

Answer 13

Converts instructions into signals, which are then sent around the CPU.

Question 14

In a decoder, how many outputs can be activated at once?

Answer 14

1, as shown in this truth table: https://b3van8qm1o7ou9d3b48qdhsg-wpengine.netdna-ssl.com/wp-content/uploads/2020/11/VHDL-Table-1.jpg (sorry for the link i have to pay to put photos in here)

Question 15

Demultiplexer

Answer 15

Uses input signals to create several outputs

Question 16

True or false: A demultiplexer is almost identical to a multiplexer

Answer 16

False! A demultiplexer’s layout is more similar to that of a decoder, but with an extra input signal.

Question 17

Identity law

Answer 17

Output is always equal to input A.
AND: 1A = A
OR: 0 + A = A

Question 18

Null law in AND form

Answer 18

Output is always 0.

0A = 0

Question 19

Null law in OR form

Answer 19

Output is always 1.

1 + A = 1

Question 20

Idempotent law

Answer 20

If all inputs are A, the output will also be A.
AND: AA = A
OR: A + A = A

Question 21

Inverse law in AND form

Answer 21

If one input is the negation of the other input, the output will be 0.
AĀ = 0

Question 22

Inverse law in OR form

Answer 22

If one input is the negation of the other input, the output will be 1.
A + Ā = 1

Question 23

Commutative law

Answer 23

Order of inputs isn’t important.
AND: AB = BA
OR: A + B = B + A

Question 24

Associative law

Answer 24

If there are 3 inputs, order isn’t important.
AND: (AB)C = A(BC)
OR: (A + B) + C = A + (B + C)

Question 25

Absorption law

Answer 25

Input and output must be the same value
AND: A(A + B) = A
OR: A + AB = A

Question 26

De Morgan’s Law

Answer 26

Negation of AND = negation of OR

A̅ +̅ B̅ = A̅B̅