How do you explain binary to me if I'm a bit 'thick'?

Question

I just dont get it! I'M MISSING THE MNEMONIC?

Answer 1

Imagine you only have two options, either there is something, or there is not. If there is something, you have a 1, if there's nothing you get a 0. If your problem is counting in binary system, try imagining you only have two fingers with which to count, that way you'll get the general idea. Keep it up!

Answer 2

Hmmm .. I may regret starting this, but here goes.

Binary numbers are based on the number two (generally written as 2 in western notation). The only numbers that "exist" in the binary system are zero (0) and the powers of 2 (1, 2, 4, 8, 16, 32, 64, 128, etc. to infinity), which I'll call the "binary set".

Any whole number can be composed by summing elements (numbers) in the "binary set". So, for example, the number six (in decimal) is the sum of the third element in the set (4) and the second element (2).

As others have pointed out, the only digits available in the binary system are 0 and 1, so it looks like we may have a problem. How can we represent the presence of the required set members with just two digits. Well, as it turns out, the problem can be solved with just a little imagination. Let us think about that 6. We know 6 is the sum of the third and second elements in the binary set. To represent this, we use the digit "1" to show when an element is present, and "0" to show that an element is not required. So, the number 6 in decimal can be represented as 110 in binary.

Look at that 110 a little closer. First thing to note is the binary number contains 3 digits, so the first digit represents the third element in the binary set. Reading from left to right, the first digit is "1", meaning the third element is required; the second digit is "1", so the second element is needed; and the third digit is "0", so the first element is not required. What does that give us? Well, the third element is 4, the second element is 2, and the first element isn't needed, so we have 4+2(+0)=6. Neat.

Now try another example. How about 11 (decimal).

Well, lets see.

11 lies between 8 and 16 (the fourth and fifth elements in the binary set), so the result will contain the fourth element. How about the third element? Well 8+4 = 12, which is greater than 11, so the third element isn't present in the binary number; but the second and first elements are present. So the result is 1011; meaning the fourth, second and first elements in the binary set are required, but the third element isn't present.

Hope this helps

Answer 3

Binary is based on only using two numbers: 0 and 1. Think about it as each digit is either turned on or off. 1 is on, and 0 is off. The right-most digit represents 1, the second one represents 2, the next one 4, the next one just keep multiplying by two. A couple of examples of binary numbers are below:

Let's look at the binary number 10011. If we write a little key, and put it in, we get:
16 8 4 2 1
1 0 0 1 1
So we have 16, 2 and 1 turned on, 8 and 4 turned off. So the number is equal to 16+2+1=19.

Another example: 11101
16 8 4 2 1
1 1 1 0 1
This time we have 16+8+4+1=29

NB Computers work using binary to store numbers. Binary is called a 'base 2' numeric system. But I won't bother explaining that, as I don't think I'd do very well. Others have tried to explain it that way if your read their answers.

Answer 4

Ordinary numbers use the decimal system with 10 different digits (0-9). The only reason that we use 10 digits is because we have ten fingers and math started by counting fingers. You could use any number of digits, not just ten, and build a complete number system from it. Binary is a number system that only uses two different digits (0-1). You can count do math, etc. in binary just like in decimal. In fact, counting in bianry is like counting in decimal except that numbers with digits greater than 1 aren't allowed.

Look at how counting goes with this rule. The first number is 1 (just like a decimal 1). Start looking for the next number that has only 1s and 0s in it. Obviouly 2,3,4,5,6 etc. are not allowed. The next allowed number is 10. Unlike in decimal where this represents ten, in binary, 10 comes right after 1 so 10 is two in binary. You can go on and count looking for the next number made up of 1s and 0s only coming up with any number you want. Here's a list of the first several:

Binary Decimal
1 -- 1
10 -- 2
11 -- 3
100 -- 4
101 -- 5
110 -- 6
111 -- 7
1000 -- 8

You can figure out how much a binary number is worth much like you can do with decimal. In decimal, 3401 is equal to 3*10*10*10 + 4*10*10 + 0*10 + 1. In binary 1101 is equal to 1*2*2*2 + 1*2*2 + 0*2 + 1 = 13. You'll notice that each higher place in the binary number has an extra 2 multiplier instead of a10 las in decimal.

So why does anyone care about binary? There are many things in science that can have two states. An electrical switch can be on or off. A magnet can be magnetized with its north pole at one end or the other. Computer memories, hard drives, etc. are built of such systems. Each piece of storage can only have one of two conditions so it represents a binary digit (bit for short). The fact that we can do math in binary as well as decimal and convert between the two is the basis for modern computers.

Answer 5

Binary is a base 2 system instead of the usual base 10 we use. By base I mean powers of 10..anything to 0 is 1, anything to 1 is itself, 2 is squared etc. so we see this in base 10 system as 1000,100,10,1.
Now in base 2 system 2 to the 0 power is 1
Now in base 2 system 2 to the 1 power is 2
Now in base 2 system 2 to the 2 power is 4
Now in base 2 system 2 to the 3 power is 8
Now in base 2 system 2 to the 4 power is 16 and so forth
Now in base 2 system 2 to the 5 power is 32 and so forth

So you take the binary number and use 1s and 0s..1 to indicate a yes and 0=no
you start at left with biggest number so if you wanted to make binary out of 30
you cannot fit 32 into it so would be 0
you can fit a 16 so it would be a 1
30-16=14
you can fit an 8 into 14 so it becomes a 1 and have 6 left
you can fit a 4 into 6 so it is a 1
you can fit a 2 into the 2 left over
number all used up so add a 0 in the 2^0 field
so 30 in binary is 011110 or drop the 1st zero and make it just 11110

Answer 6

We use positional number systems that consist of digits that can represent quantitys. Usually the least significant digit is the right most with more significant digits lined up to the left of it.

Each number system has a base. The base tells you how many things you can represent/count with one digit. You always have to start with zero or none of them (what ever you are counting) so the most you can count with one digit is the base -1.
For the decimal system base 10 , (interesting fact the base when written in the system of that base is always one zero) you can count nine thingies with one digit. If you have nine of them and you get one more the nine goes to zero and you carry one to the next most significent place, the tens place.

Binary is base 2, so you can count 2 - 1 or one thinigie with one binary digit (bit). If you get another one the 1 goes to zero and you carry one to the next most significent place the 2's place. Thats binary.

There are some other interesting base systems, the oddest perhaps is the way we count time. Starting with seconds as the least significent digit of time. Seconds are base 60. (Not having 59 special symbols to count base 60 things we use decimal numbers to represent them.) We count 59 seconds set the seconds to zero and carry one to the minutes place. Minutes are also base 60. After counting 59 minutes we set minutes to zero and carry into the hours place.
Now here it gets interesting the hours are either base 12 or base 24. If we use base 12 there is a more significent digit than hours which is binary, and oddly enough written to the right of the least significent digit of time, the seconds. This digit is AM or PM (AM = 0, we have not had a carry from the hours or PM = 1, we have had a carry from the hours). If we were consistent we would go from 11:59:59 AM Oclock to 00:00:00 PM Oclock. Who needs consistent, we are human, we eat confusion for breakfast.

When PM overflows we carry into the days digit. There are two kinds of days digits, weeks and mounths. The weeks days digit is base seven
The base seven days digit carrys into a base 52 weeks digit that carries into the years digit.
The other days digit is either base 28, 29, 30, or 31. The base depends on the month year and centuary. Months are base 12 and carry into years,
which are base ten.

The thing that is a little confusing about this is the zero. On the day that we call January the first, the day counter for the month of january is zero. We haven't actualy finished any days but we are working on the first one.

Now dosen't binary seem simple?

Answer 7

Understand how decimal works first then tackle the other number systems
Decimal is based on 10;
Most people have ten fingers, so decimal, our counting system is built around this fact. we call each finger a name one through to ten,
Electronics equipment does not have 10 fingers to count with so the number system is altered to allow numbers to be represented by the two states electronics can deal with,
this is best understood by picturing a light bulb, it can be either on or off, when it is on we will call this 1, when it is off we will call it the same as decimal zero. There are two states (bi) on or off we now call this 1 or 0
To count in binary each time we go above 1 we carry the one.
0 decimal is then equal to 0 binary
1 decimal is then equal to 1 binary
2 decimal is then equal to 10 binary (this is not ten it is the carry)
3 decimal is then equal to 11 binary (this in not eleven)
4 decimal is then equal to 100 binary (this is not on hundred)
5 decimal is then equal to 101 binary (note the pattern)
Understanding how the numbers are represented is the key to understanding binary.
Good luck keep at it one day it will all come together and you will suddenly understand it.

Answer 8

everyone is used to counting in tens. Counting up from 0 to 9 we only have a single digit but when we get past 9 we add another digit (a ten) and start the units at zero again......in fact in base 10 all numbers are made up using the numbers 0 to 9.

Counting in binary is no different in principle but is restricted to base 2 i.e. we only have zeros and ones. So starting at zero we get:-

0 =0
1 =1
10 =2
11 =3
100 =4
101 = 5

and so on. Computers use binary since this can easily be translated into a response to an electric signal eg 0=off and 1=on. From combinations of bit being on or off we are able to program the computer to carry out calculations, produce graphics, music etc etc. In the earliest days of computing people had to program the computers with very basic code (machine code and paper tapes with holes punched in them) which literally set the state of the computer bits to on or off. Today things are much more sophisticated and all the basic functions are hidden from us but when it gets down to it all we are doing is producing binary code by switching bits off and on to get teh computer to carry out work for us.

Answer 9

Hi!

The binary numeral system (base 2 numerals) represents numeric values using two symbols, typically 0 and 1. More specifically, binary is a positional notation with a radix of two.

Owing to its relatively straightforward implementation in electronic circuitry, the binary system is used internally by virtually all modern computers.

Answer 10

Decimal uses 10 numbers 0 through 9.
Binary uses 2 numbers 0 and 1

In Decimal when you get to 9 you have to had another column
In Binary when you get to 1 you have to add another column

Bin = Dec

00 = 00
01 = 01
10 = 02
11 = 03