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For example, 5246 can be expressed like in the following expressions

5246 =5 × 10 3 + 2 × 10 2 + 4 × 10 1 +6 × 10 0 = 5 × 1000 + 2 × 100 + 4 × 10 + 6 × 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=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@703F@

The place-value of any place to the right of the decimal point is a fraction computed from a product in which the reciprocal of the base—or a fraction with one in the numerator and the base in the denominator—is repeated as a factor exactly as many times as the place is to the right of the decimal point.

For example

254.68 = 2 × 10 2 + 5 × 10 1 + 4 × 10 0 + 6 × 10 1 + 8 × 10 2 = 200 + 50 + 4 + 6 10 + 8 100 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=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@6DD5@

Binary system

The binary number system is base 2 and therefore requires only two digits, 0 and 1. The binary system is useful for computer programmers, because it can be used to represent the digital on/off method in which computer chips and memory work.

A binary number can be represented by any sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states.

Counting in binary is similar to counting in any other number system. Beginning with a single digit, counting proceeds through each symbol, in increasing order. Decimal counting uses the symbols 0 through 9, while binary only uses the symbols 0 and 1.

When the symbols for the first digit are exhausted, the next-higher digit (to the left) is incremented, and counting starts over at 0A single bit can represent one of two values, 0 or 1.Binary numbers are convertible to decimal numbers.

Here's an example of a binary number, 11101.11 ( 2 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaigdacaaIXaGaaGymaiaaicdacaaIXaGaaiOlaiaaigdacaaIXaWaaSbaaSqaaiaacIcacaaIYaGaaiykaaqabaaaaa@3DF1@ , and its representation in the decimal notation

235.64 ( 8 ) = 2 × 8 2 + 3 × 8 1 + 5 × 8 0 + 6 × 8 1 + 4 × 8 2 = 157.8125 ( 10 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=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@6396@

Hexadecimal system

The hexadecimal system is base 16. Therefore, it requires 16 digits. The digits 0 through 9 are used, along with the letters A through F, which represent the decimal values 10 through 15. Here is an example of a hexadecimal number and its decimal equivalent:

34 F 5 C ( 16 ) = 3 × 16 4 + 4 × 16 3 + 15 × 16 2 + 5 × 16 1 + 12 × 16 0 = 216294 ( 10 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=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@657F@

The hexadecimal system (often called the hex system) is useful in computer work because it is based on powers of 2. Each digit in the hex system is equivalent to a four-digit binary number. Table below shows some hex/decimal/binary equivalents.

Hexadecimal Digit Decimal Equivalent Binary Equivalent
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
A 10 1010
B 11 1011
C 12 1100
D 13 1101
E 14 1110
F 15 1111
10 16 10000
F0 240 11110000
FF 255 11111111

Octal system

Binary is also easily converted to the octal numeral system, since octal uses a radix of 8, which is a power of two (namely, 23, so it takes exactly three binary digits to represent an octal digit). The correspondence between octal and binary numerals is the same as for the first eight digits of hexadecimal in the table above. Binary 000 is equivalent to the octal digit 0, binary 111 is equivalent to octal 7, and so forth.

Converting from octal to binary proceeds in the same fashion as it does for hexadecimal:

65 ( 8 ) = 110 1012 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaiAdacaaI1aWaaSbaaSqaaiaacIcacaaI4aGaaiykaaqabaGccqGH9aqpcaaIXaGaaGymaiaaicdacaaMe8UaaGymaiaaicdacaaIXaGaaGOmaaaa@4161@
17 ( 8 ) = 001 1112 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaigdacaaI3aWaaSbaaSqaaiaacIcacaaI4aGaaiykaaqabaGccqGH9aqpcaaIWaGaaGimaiaaigdacaaMc8UaaGjbVlaaigdacaaIXaGaaGymaiaaikdaaaa@42E9@

And from octal to decimal:

235.64 ( 8 ) = 2 × 8 2 + 3 × 8 1 + 5 × 8 0 + 6 × 8 1 + 4 × 8 2 = 157.8125 ( 10 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=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@6396@

Converting from decimal to base–b

To convert a decimal fraction to another base, say base b, you split it into an integer and a fractional part. Then divide the integer by b repeatedly to get each digit as a remainder. Namely, with value of integer part = d n 1 d n 2 ... d 2 d 1 d 0 ( 10 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaaWcbaGaamOBaiabgkHiTiaaigdaaeqaaOGaamizamaaBaaaleaacaWGUbGaeyOeI0IaaGOmaaqabaGccaGGUaGaaiOlaiaac6cacaWGKbWaaSbaaSqaaiaaikdaaeqaaOGaamizamaaBaaaleaacaaIXaaabeaakiaadsgadaWgaaWcbaGaaGimaiaacIcacaaIXaGaaGimaiaacMcaaeqaaaaa@47BF@ , first divide value by b the remainder is the least significant digit a 0 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadggadaWgaaWcbaGaaGimaaqabaaaaa@37AE@ . Divide the result by b, the remainder is a 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadggadaWgaaWcbaGaaGymaaqabaaaaa@37AF@ .Continue this process until the result is zero, giving the most significant digit, a n 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadggadaWgaaWcbaGaamOBaiabgkHiTiaaigdaaeqaaaaa@398F@ . Let's convert 43868 ( 10 ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaaisdacaaIZaGaaGioaiaaiAdacaaI4aWaaSbaaSqaaiaacIcacaaIXaGaaGimaiaacMcaaeqaaaaa@3C9B@ to hexadecimal:

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Introduction to computer science. OpenStax CNX. Jul 29, 2009 Download for free at http://cnx.org/content/col10776/1.1
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