Propositional Logic and Circuits

Question 1

Compound Proposition

Answer 1

A proposition built from an atomic proposition:
Logic is easy -> Logic is not hard

Question 2

|=

Question 3

⊥

Answer 3

Special proposition, which is false under every interpretation

Question 4

Modus Ponens

Answer 4

Direct Proof

Question 5

Reductio Ad Absurdum

Answer 5

Proof by contradiction

Question 6

Modus Tollens

Answer 6

If p implies q, and q is false, then p is false.

Question 7

Case Analysis

Question 8

Logic Equivalent

Answer 8

P ≡ Q
Same truth values under every possible interpretation/ same DNF.

Question 9

Disjunctive Normal Form

Answer 9

The values where the truth table’s result is true.

Question 10

Equivalence

Answer 10

Same output considering same inputs.

Question 11

≡

Answer 11

Reflexive, Transitive, Symmetric

Question 12

T

Answer 12

True for everything.

Question 13

Sequential Gate

Answer 13

Can loop back round in on itself.

Question 14

Latch

Answer 14

A flip/flop circuit
Mostly remains 0, but you can supply something to make it 1.

Question 15

Two’s Complement

Answer 15

Converting a positive binary number to a negative one.

Question 16

Half Adder
Full Adder

Answer 16

Half Adder - The half adder circuit has two inputs: A and B, which add two input digits and generates a carry and a sum.
Full Adder - A full adder takes two binary numbers plus a carry or overflow bit. The output is a sum and another carry bit.

Question 17

Scientific Notation (Standard Form)

Answer 17

10^3 = 1000, so 4 × 10^3 = 4000

Question 18

Binary Fractions

Question 19

Positional system

Answer 19

Multiply each digit by its place value

Question 20

Floating Point Numbers

Answer 20

Hell