A Proposition is a declarative sentence, which may be shown to be either true, or false, whether the statement is true or false is not – however – relevant. Both “1+2-=3″ and “1+2=4″ are example of propositions. Predicate logic allows us to explore the truthfulness of a statement, it has an expressive power which propositional logic does not.
We can apply the normal rules of arithmetic to binary, just as we can to any other number system – and the only time this can get a little complicated is when considering binary subtraction – or negative binary since strictly the negative sign should not be used.
We are used to working with the concept that there are 10 unique numerical digits, 0 to 9, however due to the boolean nature of logic circuits, computers tend to operate using just the digits 0 and 1, the binary number system.
Boolean Algebra is a two state system of algebra, we can apply this to the binary number system where only two valid numeric symbols exist, “1″ and “0″ and thus use boolean logic to solve binary problems. The electronics inside a computer rely on this system, modeling voltage in a connection as either on (1, or TRUE) or off (0, or FALSE).