Binary number system

Our journey from the smallest to the largest dimensions of interest to scientists has thus covered over 60 powers of 10. 

In the familiar decimal or base 10 number system, a typical number such as 1234.56 is explicitly represented by 

The base 10 number system probably evolved from the fact that we have 10 Angers. The binary or base 2 number system uses just two digits, 0 and 1. It is like we use our two hands rather than our fingers to count. A binary number b ib2b bQ.b-ib-2 is given by the analog of Eq. (2.6) 

Here are first few decimal numbers and their binary equivalents  

It is common practice to write binaries in groupings of four digits. The length of binary numbers might appear unwieldy compared to their decimal equivalents, but computers like them just fine. 

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Bit. As it has already been stated above that each digit of binary number system is known as Binary Digit . To make its name short, the B has been taken from Binary and IT is derived from Digit, thus making its name as BIT. A bit represents the smallest part of memory locations in computer, which stores either 0 or 1. Refer figure (3) for bit. 

Decimal to binary conversion. The base of binary number system is 2 because it uses only two digits to represent the number. The base of decimal number system is 10 because total 10 digits are used to represent the... 

Hexadecimal to decimal conversion. The system of number conversion from hexadecimal to decimal system is same as from binary to decimal and octal to decimal. The difference is only of their base value because binary number system has its base value as 2, octal has 8 and hexadecimal has 16. This can be understood by the following problem. 

Although place-value systems make it easier for people to do arithmetic, they also help computers perform electronic computations at blinding speeds. A common place-value system used in computers is the binary number system, which is a base 2 system. The binary system has two values 0 and 1. These values correspond with the signals high and low in the electronic circuits of computers. Because these numbers are so simple, computers can process them electronically up to a trillion times per second, depending on the speed of the computer. 

Before we can discuss the details of the binary numbering system, you must understand a couple of things. First of all, the binary numbers 0 and 1 are not the same as they are in the decimal number systems. Instead, they are just placeholders. They could just have easily been called A and B. Second, we use a few special words to categorize binary numbers ... 

All information handled or generated by the central processing unit (CPU) must be binary or binary-coded machine language. This includes instructions, memory addresses, and data. Thus, the small-computer user must quickly become familiar with this number system. It would be well to review here the binary number system and binary arithmetic. 

The most commonly used ADC output format is the binary number system, because it is directly compatible with many digital computers. Other codes, usually binary coded decimal, are sometimes used. In addition, bipolar input-converters such as the 1 V or 10 V units can have different forms of binary coding to account for the dual polarity. 

Most htde kids know the sequence of doubled numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 — These are, of course, successive powers of 2. Since the internal workings of computers is based on the binary number system, a memory capacity of 2 ° = 1024 bytes is conventionally called 1 kilobyte and a CPU speed of 1024 hertz is 1 kilohertz. Likewise, multiples of 2 ° = 1048576 1.05 x 10 are called megabytes (MB) and... 

Logarithms to the base 2 can be associated with the binary number system. The value of log2 x (also written as Ig 2) is equal to the number of bits contained in the magnitude x. For example, log2 64 = 6. 

Bit Binary digit, of which there are only two, the numbers zero and one. Computer technology is based on the binary number system because early computers contained switches that could be only on or off. 

Microelectronics involves digital solid state integrated circuits mounted on single crystal pieces of silicon called chips. The digital system used is binary which means that there are only two numbers involved (0 and 1). This is quite different from the conventional decimal number system where all members consist of combinations of 0 and 1 to 9. Figure 15.9 shows a few numbers in the decimal system together with their binary equivalents. Addition, subtraction, multiplication, and division are much simpler to perform in the binary number system than in the decimal system. 

Consider a Turing computable function f(i) that maps the positive integers IN onto a subspace of IN. Then we know from the previous section that there is a quantum Turing machine based on a reversible, classical machine M on which this function can be evaluated. The overall computation of / is described by the unitary operator Uf which is the product of local, unitary transformations Ui. To abbreviate the notation, we will only consider the subspace of the input and output data of the quantum machine. Furthermore, we will write i) to denote a part of the memory in which the number i is stored. For example, using the binary number system,... 

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