How boolean algebra helps modern computer?

Answer 1

George Boole developed a mathematical notation which is suited to the analysis or design of switching.

a) a switch may be only on or off

b) assume 1 equals on, and 0 equals off

Example: two switches in series,

if both are on will have a combined value of 1.

Boolean 1 + 1 = 1 (aka and + and = and)

if one switch were on and the other off, the combination is 0

Boolean 1 + 0 = 0 (aka and + not = not) nand is 'not and'.

if both switches were off, then the combined value is off.

Boolean 0 + 0 = 0 (aka not + not = not)

You may perform a similar analysis for a pair of switches in parallel.

c) the truth values given are arbitrary. The logic system will work equally well if 1's are replaced with 0's and vice versa but the truth tables will differ.

From such simple beginnings, a sufficient logic system may be built to solve problems that can be expressed as equations.

This is called 'machine language' in its simplest form.