George Boole (1815-1864) was born to a low class family and only received an elementary school education. Despite that, he taught himself highly advanced mathematics and different languages as a teenager without any assistance. He started teaching at age sixteen, and started his own school at age nineteen. By his mid-twenties, he had mastered most of the important mathematical principles in his day.
A Crucial Turning Point For Computers
One of the most important discoveries for computer science is the development of boolean logic. It was a concept thought up by a genius mathematician named George Boole (1815-1864). Boole had the idea that his algebra could be used to solve logical problems. From around 1844 to 1854, he developed the fundamentals of what is now called boolean logic (also known as boolean algebra). Boole's system is based on binary numbers, a 0 and 1, along with the three most basic and incredibly powerful operations still used today: AND, OR, and NOT.
George Boole's idea was revolutionary. Ironically, however, it was mostly criticized or ignored by his peers despite George Boole's great reputation. Fortunately, a few were open-minded enough to consider the idea. Charles Sanders Peirce, an American logician, spent 20 years modifying and expanding Boole's original system. He soon realized the immense potential it had if it were applied to digital circuitry. While he never actually applied the theory himself, a young student named Claude Shannon picked the idea up and did.
George Boole ended up dying at the age of 49 due to a strong sense of duty without ever even imagining the enormous breakthrough he discovered. In essence, George Boole was a remarkable prodigy restricted due to being born during the wrong time, place, and social class.
George Boole's idea was revolutionary. Ironically, however, it was mostly criticized or ignored by his peers despite George Boole's great reputation. Fortunately, a few were open-minded enough to consider the idea. Charles Sanders Peirce, an American logician, spent 20 years modifying and expanding Boole's original system. He soon realized the immense potential it had if it were applied to digital circuitry. While he never actually applied the theory himself, a young student named Claude Shannon picked the idea up and did.
George Boole ended up dying at the age of 49 due to a strong sense of duty without ever even imagining the enormous breakthrough he discovered. In essence, George Boole was a remarkable prodigy restricted due to being born during the wrong time, place, and social class.
What is the Big Deal?
George Boole saw his ideas solely as a way to prove logical arguments using mathematics. A simple example of this is to state that "The stars are the suns and the planets." Boole used that to represent an equation where x represents the stars, y represents the suns, and z represents the planets.
x = y + z
If the stars are combined of both the suns and the planets, then therefor if you take all the stars and subtract all the planets, then we are left with only the suns. After representing the statement, we have two equations that are supported with mathematical laws.
x - z = y
Albeit his ideas are quite interesting to think about, they certainly don't look important. Sure, Boole showed that the equation x(1-x) = 0 proves that an individual cannot be both a man and not a man at the same time, but that isn't too spectacular. It certainly doesn't seem like a ground breaking discovery to prove a statement using a math equation.
A majority of academics also disregarded George Boole's boolean logic, despite Boole's immense respect among others. Charles Peirce was one of the few who remember his words, and ended up looking beneath the surface of his ideas. Twelve years after Boole published his system, Peirce briefly described Boole's ideas. Sometime during the next twenty years, Peirce found out that boolean logic can be used in electrical circuits, which is used in not only computers but also simple devices like a light switch. Unfortunately, it wasn't until another fifty years that such a design is actually made.
x = y + z
If the stars are combined of both the suns and the planets, then therefor if you take all the stars and subtract all the planets, then we are left with only the suns. After representing the statement, we have two equations that are supported with mathematical laws.
x - z = y
Albeit his ideas are quite interesting to think about, they certainly don't look important. Sure, Boole showed that the equation x(1-x) = 0 proves that an individual cannot be both a man and not a man at the same time, but that isn't too spectacular. It certainly doesn't seem like a ground breaking discovery to prove a statement using a math equation.
A majority of academics also disregarded George Boole's boolean logic, despite Boole's immense respect among others. Charles Peirce was one of the few who remember his words, and ended up looking beneath the surface of his ideas. Twelve years after Boole published his system, Peirce briefly described Boole's ideas. Sometime during the next twenty years, Peirce found out that boolean logic can be used in electrical circuits, which is used in not only computers but also simple devices like a light switch. Unfortunately, it wasn't until another fifty years that such a design is actually made.
On December 30th, 1886, Charles Peirce sent his design of a digital circuit using boolean logic to an associate, Allan Marquand. Where as in the figure to the left would require both points A, B, and C for there to be a circuit, the figure to the right would require A, B, or C to be a circuit.
How 1's and 0's Are Used In Logic Gates
Logic gates are the core of boolean logic. Yet while the gates basic functions are simple to comprehend, they can form complex patterns capable of amazing feats. A simple, yet very powerful tool.
Simple Boolean Logic
0 = False 1 = True
The AND gate outputs true only when inputs A and B are also true
The OR gate outputs true only when one or both of the inputs are true
The Exclusive OR gate outputs true only when one input is true, and the other false
The NOR gate outputs true only when both inputs are false
The NAND gate outputs true only when one or both of the inputs are false
The NOT gate outputs the opposite of the input (( 0 -> 1 ::: 1 -> 0 ))
Note: You can connect the gates together. For example, one of the OR gates input can be an AND gates output.
0 = False 1 = True
The AND gate outputs true only when inputs A and B are also true
The OR gate outputs true only when one or both of the inputs are true
The Exclusive OR gate outputs true only when one input is true, and the other false
The NOR gate outputs true only when both inputs are false
The NAND gate outputs true only when one or both of the inputs are false
The NOT gate outputs the opposite of the input (( 0 -> 1 ::: 1 -> 0 ))
Note: You can connect the gates together. For example, one of the OR gates input can be an AND gates output.