The short answer: hardware and the laws of physics. Every number in your computer is an electrical signal, and in the early days of computing, electrical signals were much harder to measure and control very precisely. Essentially, it only allows current to flow from the source to the drain if there is a current in the gate.
This forms a binary switch. Manufacturers can build these transistors incredibly small—all the way down to 5 nanometers, or about the size of two strands of DNA.
Gates take two inputs, perform an operation on them, and return one output. This brings us to the long answer: binary math is way easier for a computer than anything else. Boolean logic maps easily to binary systems, with True and False being represented by on and off. Two inputs are easy to manage. A binary truth table operating on boolean logic will have four possible outputs for each fundamental operation. But because ternary gates take three inputs, a ternary truth table would have 9 or more.
Who knows? In the future, we could begin to see ternary computers become a thing, as we push the limits of binary down to a molecular level. For now, though, the world will continue to run on binary.
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Browse All Privacy and Security Articles Browse All Linux Articles Browse All Buying Guides. Best iPhone 13 Pro Case. Best Bluetooth Headphones for Switch. Best Roku TV. Best Apple Watch. Best iPad Cases. At this low level, instructions are basic arithmetic functions such as add, subtract and multiply involving the contents of memory locations and registers a cell which can have arithmetic operations carried out on it.
A programmer can also write code in assembly language. This is a low level language comprising instructions known as mnemonics which are used to move data between registers and memory and perform arithmetic operations.
Boolean algebra, developed by the British mathematician George Boole in the 19th century, is a branch of mathematics which deals with variables which can only have one of two states, true or false. In the s Boole's work was discovered by the mathematician and engineer Claude Shannon, who realized it could be used to simplify the design of telephone switching circuits.
These circuits originally used relays which could be either on or off, and the desired output state of the system, depending on the combination of states of the inputs, could be described by a Boolean algebraic expression. Boolean algebra rules could then be used to simplify the expression, resulting in a reduction of the number of relays required to implement a switching circuit.
Eventually Boolean algebra was applied to the design of digital electronic circuitry as we will see below. The most basic processing element in a digital electronic circuit or computer is a gate. A gate takes one or more digital signals and generates an output. In their simplest form, small groups of gates are available on a single IC. However, a complex combinational logical function can be implemented using a Programmable Logic Array PLA and more sophisticated devices such as microprocessors are composed of millions of gates and memory storage cells.
Boolean algebraic expressions can be used to express what the output signal of a circuit should be, depending on the combination of inputs. The main operations in Boolean algebra are and , or and not. During a design process, the required value of an output for all the various permutations of input states can be tabulated in a truth table. Once a truth table is created, a Boolean expression can be written for the output, simplified and implemented using a collection of logic gates.
So a typical Boolean expression with three independent variables A, B and C and one dependent variable D would be:. Truth table for a simple digital circuit. Answer: -1 or other negative numbers are normally implemented using two's complement. So to represent -1 in two's complement form, invert the bits and add Remember this is just a conventional way of representing a negative number in a digital system so that arithmetic can be done and work out ok.
Because only three bits are used, the 4th bit would be "unseen" by the digital system and the result in this example would be interpreted as or zero. Question: Which characteristic of a transistor is useful for digital counting and manipulation, and why?
Answer: A transistor can behave as a controlled switch and form part of an elementary circuit element called a flip-flop. A flip-flop can store one bit of information, and in addition to other circuit elements, a higher level device called a binary counter can be implemented. Answer: It depends on the technology. Sometimes a voltage close to zero is used for logic 0 and a higher voltage is used for logic 1.
However in the case of some serial data transmission standards, a negative voltage represents logic 1 and a positive voltage represents logic 0. Several voltage levels are used by digital integrated circuits chips , e. Answer: Binary encoding is a system of transmitting binary data over a link designed to handle text data. If you mean how do I represent 16 decimal in the octal numbering system base 8 , the answer is 20 2 in the "eights" place.
Answer: "1" and "0" by convention represent "high" and "low" in a digital circuit. The article was really helpful for my studies.. You did it very well. Thank you very much for the information. In the time before sophisticated computer graphics and when displays could only show text, alphanumeric characters were displayed on screen using a chip called a character generator ROM Read Only Memory. This converted ASCII bytes in memory into a rectangular matrix of dots representing the character that circuitry in the computer and monitor could display.
Nowadays everything you see on screen is stored as a raster image in memory with three bytes for each pixel you see on screen. One byte is for red, one for blue and one for green. This is probably a bit confusing for you, but the good news is that this concept is explained in detail here. We finally come to the million-dollar question: why do computers use binary numbers?
Nevertheless, we will try our best to come up with answers that sound logical and support the use of binary numbers by computers.
To present numerical data in our daily life, we use the decimal number systems. Instead, computers represent numbers by using the lowest base number system used by us, which is two. This is the binary number system. Computers use voltages and since voltages changes often, no specific voltage is set for each number in the decimal system.
For this reason, binary is measured as a two-state system i. Also, to keep calculations simple and convert into binary online , computers use the binary number system. But, thanks to the binary system, only four rules are required by the computers for calculations.
Last but not the least, a major reason computers use the binary system is that the two-state system is the number system best suited to the optical and magnetic storage components of the computer. If you take only a quick glance at both, you will immediately assume that the binary system takes up more space than the decimal system.
The reason many people assume that the binary system takes more space than the decimal system is because of the way the former is written on the computer screen. You can always decrease the number of digits used for representing a number by increasing the base, but it is simply impossible to create a digital circuit that uses anything other than two as base to operate. So, ready to convert into binary online? With the help of switches, you can encode numbers into binary format.
This system could be used by several digital devices including watch, digital TV decoder box, calculator, burglar alarm, cell phone and a computer. In the memory, values are stored in binary format. Suppose a bank of eight rocker switches were available to you and depending on whether it is on or off, each switch could represent 0 or 1.
Someone else would be able to read the number if they looked at the switches. Transistors are used in computers to implement switches. It is the single bit—something we touched upon earlier. Only a single switch is required to implement this configuration memory. You get a byte when eight switches are combined together. Convert into binary online to get a better understanding of this. The switches can be set on and off by the digital hardware.
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