Can someone help me understand binary language?

Question

Studying this and it isn't making any sense. Help!

Answer 1

Our usual number system (decimal) is base 10. That means there are 10 'digits' that make up a representation of a number: 0,1,2,3,4,5,6,7,8, and 9.

Each digit's position in a number's representation is indicitive of an order of that number system's values. So, for example, look at the decimal number: 123.45

They are 5 digits in that number, each occupying a different order of power (i.e. magnitude). So, the 1 is in the 100's spot, the 2 is in the 10's spot, the 3 is in the 1's spot, the 4 is in the tenths spot, and the 5 is in the hundredths spot. In order to get the VALUE of the number, you take each digit and multiply it by the order value.

So 123.45 = 100 * 1 + 10 * 2 + 1 * 3 + 1/10 * 4 + 1/100 * 5

Why all this nonsense? Because binary is exactly the same except that there are only TWO digits in that number system: 0 and 1

So, when determining the value of a binary number (i.e. converting it into decimal), you have to take the position of the digit in the representation in order to figure it out. Note that in most cases, binary numbers usually only represent whole (i.e. natural) numbers, though they can be used to represent negative and Real numbers in some computer representations.

Since there are only 2 digits in binary, the order/magnitude is based on 2's, instead of 10's for decimal.

Another way to think of the orders of value for decimal is in powers of 10's. So, in the example above:
123.45 = 10^2 * 1 + 10^1 * 2 + 10^0 * 3 + 10^-1 * 4 + 10^-2 * 5
= 10*10 * 1 + 10 * 1 + 1 * 3 + 1/10 * 4 + 1/100 * 5

In binary, just replace the 10's with 2's.

So, for example, the binary number 10110 can be converted to decimal this way:

(2^4 * 1) + (2^3 * 0) + (2^2 * 1) + (2^1 * 1) + (2^0 * 0) =
(2*2*2*2 * 1) + (2*2*2 * 0) + (2*2 * 1) + (2 * 1) + (1 * 0) =
(16 * 1) + (6 * 0) + (4 * 1) + (2) + (0) =
16 + 0 + 4 + 2 + 0 =
22

There you have it!

Answer 2

Binary - So Simple a Computer Can Do It

While every modern computer exchanges and processes information in the ones and zeros of binary, rather than the more cumbersome ten-digit decimal system, the idea isn't a new one.

Australia's aboriginal peoples counted by two, and many tribes of the African bush sent complex messages using drum signals at high and low pitches. Morse code, as well, uses two digits (dots and dashes) to represent the alphabet.

Gottfried Leibniz laid the modern foundation of the movement from decimal to binary as far back as 1666, while John Atanasoff, a physics professor at Iowa State College, had built a prototype binary computer by 1939.

In the meantime, Claude Shannon, Konrad Zuse and George Stibitz had been pondering away in their own corners of the world, musing on the benefits of combining binary numbers with boolean logic.


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Today, of course, and in almost every computer built since the 1950s, the binary system has replaced the decimal (which really only came about because it was handy to be able to count on your fingers) and advanced digital computer capabilities to an incredible degree.

Basically, binary simplifies information processing. Because there must always be at least two symbols for a processing system to be able to distinguish significance or purpose, binary is the smallest numbering system that can be used.

The computer's CPU need only recognise two states, on or off, but (with just a touch of Leibniz' mysticism) from this on-off, yes-no state all things flow - in the same way as a switch must always be open or closed, or an electrical flow on or off, a binary digit must always be one or zero.

If switches are then arranged along boolean guidelines, these two simple digits can create circuits capable of performing both logical and mathematical operations.

The reduction of decimal to binary does increase the length of the number, a lot, but this is more than made up for in the increase in speed, memory and utilisation.

Especially utilisation. Remember, computers aren't always dealing with pure numbers or logic. Pictures and sound must first be reduced to numerical equivalents that, in turn, have to be decoded again for the end result.


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So, how does it work?

It's not so very difficult, really. Binary numbers use the same rules as decimal - the value of any digit always depends on its position in the whole number.

It all gets down to bases. Decimal uses base ten, so that every time a number moves one position to the right in a figure, it increases by a power of ten (eg. 1, 10, 100 etc). Binary, on the other hand, uses base two, so each move to the right increases the value by a power of two (eg. 1, 2, 4 etc).

To convert from decimal to binary, or the other way around, you need only look at the figure's place in the whole number and add up it's value.

Simple.


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Binary vs decimal

Decimal
10 1

0

1

2

3

4

5

6

7

8

9
1 0
Binary
8 4 2 1



0



1


1 0


1 1

1 0 0

1 0 1

1 1 0

1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
Because binary uses base two as opposed to the decimal base ten, the numbers get larger much more quickly, but they still obey the same principles.
In this case, the number ten is represented by 10 (no 1s, one x 10) in decimal, and 1010 (no 1s, one x 2, no 4s, one x 8) in binary.




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Conversion

To convert a decimal number to binary, you need only keep subtracting the largest power of two. Here the decimal 200 is represented by 11001000 (one x 128, one x 64, no 32s, no 16s, one x 8, no 4s, no 2s, no 1s)

From binary to decimal is even easier - just add up the columns.


Decimal
100 10 1
2 0 0
2 x 100 + 0 + 0 = 200

Binary
128 64 32 16 8 4 2 1
1 1 0 0 1 0 0 0
1 x 128 + 1 x 64 + 0 + 0 + 1 x 8 + 0 + 0 + 0 =200



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Addition

Again, addition differs only from decimal in that it is using base two.







+ Decimal
100 10 1
2 0 0

5 0
2 5 0





+ Binary
128 64 32 16 8 4 2 1
1 1 0 0 1 0 0 0
0 0 1 1 0 0 1 0
1 1 1 1 1 0 1 0


The only trick here is to remember that it is base 2 - whereas in decimal 1 + 1 = 2 with nothing to carry into the next column, in binary, 1 + 1 still = 2, but that 2 is carried forward (as a 1, naturally).







+ Decimal
10 1

1

1

2





+ Binary
2 1

1

1
1 0



Related:
Gottfried Wilhelm Leibniz
What's So Logical About Boolean Algebra?

Answer 3

To understand a binary number you must first understand how a decimal number is constructed. Example take the decimal number 111. Since it is decimal we use powers of 10 to evaluate it.

1 x 10^2 + 1 x 10^1 + 1 x 10^0 adding these we get

100 + 10 + 1 = 111, where 10^0 always equals 1

With a binary number we do the same thing except we use the number 2 instead of 10. Using the binary number 111, we evaluate like this

1 x 2^2 + 1 x 2^1 + 1 x 2^0 any number to the 0 power is 1

4 + 2 + 1 adding up binary number 111 equals decimal number 7.

Answer 4

Think of this: 1 = yes, 0 = no. Fairly simple. With these parameters, think of all of the powers of two:
2^0 = 1
2^1 = 2
2^2 = 4
etc.
now, from right side to left side are questions about a number. consider the following:
100
In binary, you ask the following:
is there a 2^0? since the spot on the right is a 0, the answer is no. Is there a 2^1? Since the second spot is a 0, you answer no again. Is there a 2^2? Since the third spot is a 1, you answer yes. So we add up all the yes answers and get 2^2 + 0 = 4

101 would be 2^0 + 2^2 = 5
111 = 2^0 + 2^1 + 2^2 = 7

Hope that helps!

Answer 5

Take a look at this website-explains the binary system compared to the decimal system.

Answer 6

There are 10 kinds of people in the world... those who understand binary and those who don't!!! :-D

Answer 7

the processor (additionally noted as CPU) gets its classes for a variety of supplies, the working gadget (abode windows, Linux, Openbsd), additionally it gets some from the BIOS or firmware of the main board, soundcard, video card, Any application you're working additionally provides classes to the processor. and likewise definite a processor does paintings in binary, the two a sign (a million) or no sign (0).

Answer 8

http://memory-alpha.org/en/wiki/Binary_language

Answer 9

ooo10000110010000110011