To realize how crucial this system is for computers, one need not look any further than the existence of Logical Operators in most programming languages: the AND, OR, and NOT operators.
These decisions result in our computers taking a particular course of action instead of another. Modern computers use this form of logic to make decisions all the time. All logical operations result in only one of these two binary values. True is represented by 1 and false is represented by 0. Boolean logic deals with only two possible values: true or false. This is known as Boolean logic, formulated by the English mathematician George Boole during the 19th Century.īoole developed a system of arithmetical and logical operations that utilize the binary system of numbers. Boolean Logic: Using Binary Numbers to Understand Computer LogicĬomputer programs use a very specific system of logic to carry out their instructions. In the sections that follow, we will take a brief look at some of the different ways computers use binary symbols to perform some of its most fundamental operations.
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Understanding binary numbers can thus help us understand some of the fundamentals of computer operations at a sufficiently abstract level, even though our feeble human intellect might never allow us to understand the full complexity of computer operations.Īnd that is just as well, for working with simplified and abstract conceptions of computer operations is more than adequate for us students of computer science. We could combine these three outputs to get a value of 100, which in binary is the same as the number 4. Suppose the next two flip-flops have low-voltage outputs 0. There are special electronic circuits, such as flip-flops and other circuits, that can "store" or retain these specific patterns of electrical signals for extended use.įor instance, one flip-flop may have a number of inputs that currently has a high voltage output (which we interpret as 1).
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These systems could be binary logic (restricted only to true or false values), base-2 number representation of numerical values, or using other systems that rely on a series of binary numbers to represent text, pictures, or sounds.Įssentially, our computers use a series of high-voltage and low-voltage electrical signals (binary values) to represent everything from texts and numbers to images and sounds. With this method of operating and interpreting electronic circuits in place, we can proceed to design coded systems based on the binary bits to aid in our computational tasks.
This broad generalization reduces the range of interpretation of each electric signal into two distinct values, instead of an infinite range of continuous voltage values. If it is on, it is interpreted as having a value of 1.
If the bulb is off, that state is interpreted as having the value 0. An easier way of thinking about this is to imagine a light bulb. In order to design a computer that runs efficiently, we need a system that can interpret electrical signals in a simplified and effective manner.Ī good way of doing this is to interpret electrical signals as binary values: 0 for a low voltage value and 1 for a high voltage value. Perhaps it would be easier to understand all of this if we can understand the basic working of computers at the machine level.Ġ's and 1's: Interpreting the Workings of Computer CircuitryĬomputers operate on the electrical signals generated by these circuits. An example of this would be the representation of the numbers 0, 1, 2, 3, and 4 in three binary digits as 000, 001, 010, 011, and 100 respectively.īut what does this all mean at the fundamental level of computing? Why is the binary number system used as the foundation for all of our computing? Or they could be used to represent ordinary numbers as combinations of 1's and 0's. These two numbers can represent a variety of things.įor example, in computer logic, 0 represents "false" while 1 represents "true". In the binary number system, these two objects are the numbers 0 and 1. The term 'binary' means something that has only two possible objects or states. And what could be more fundamental to modern computing than binary mathematics? While possessing a vast knowledge of mathematics is not necessary to learn computer programming, it certainly helps to have a basic grasp of some of the foundational mathematics that makes computing possible.
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