On the computer system what is the difference of binary and decimal?

Answer 1

There is no difference. Decimal notation is merely a human convenience. The same rules that apply to decimal also apply to binary, the only difference being that decimal has 10 digits and deals with powers of 10, while binary uses 2 digits and deals with powers of 2. Binary (base-2) is the most primitive form of numeric notation and by far the simplest to implement at the machine level.

Answer 2

The only real difference is the number of symbols used to represent a single digit. In decimal, there are ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. But in binary there are only two symbols: 0 and 1. As a result of this, the positional value of each digit has to change. This positional value is directly related to the base.

The least-significant digit of any natural number is always the units digit. It makes no difference what base we are working in, a unit is always 1. This is because the least-significant digit represents the value (digit * base^0) and base^0 is always 1 (any number raised to the power zero is one). As we move through the digits towards the most-significant digit, we increase the power by 1. So working right-to-left, we get the following position values for each digit:

digit * base^0,

digit * base^1,

digit * base^2,

digit * base^3, and so on...

When we work with fractions, the powers decrease by 1 as we work from left to right after the dot separator. Thus we get the following position values:

digit * base^-1

digit * base^-2

digit * base^-3, and so on...

If we take the symbol 1011, in decimal we would get:

1 * 10^0 = 1 * 1 = 1

1 * 10^1 = 1 * 10 = 10

0 * 10^2 = 0 * 100 = 0

1 * 10^3 = 1 * 1000 = 1000

Adding these up we can see that 1011 decimal is one-thousand-and-eleven.

In binary, 1011 gives us:

1 * 2^0 = 1 * 1 = 1

1 * 2^1 = 1 * 2 = 2

0 * 2^2 = 0 * 4 = 0

1 * 2^3 = 1 * 8 = 8

Adding these up we can see that 1011 binary is eleven.

This works for any base. In octal (base-8) we get:

1 * 8^0 = 1 * 1 = 1

1 * 8^1 = 1 * 8 = 8

0 * 8^2 = 0 * 64 = 0

1 * 8^3 = 1 * 512 = 512

Thus 1011 octal is five-hundred-and-twenty-one.

In hexadecimal (base-16), we get:

1 * 16^0 = 1 * 1 = 1

1 * 16^1 = 1 * 16 = 16

0 * 16^2 = 0 * 256 = 0

1 * 16^3 = 1 * 4096 = 4096

Thus 1011 hexadecimal is four-thousand-one-hundred-and-thirteen.

Answer 3

The Binary system is a system that allows for the use of 1s and 0s to represent numerical values in the Base 10 system or Decimal System. For example:-

10 would be represented as 1010

Computers Use the Binary system as it is the quickest form of open and closing a switch 1 is Open is 0 is Off. Although computer languages Differ from Pascal to C++, it is all in an attempt to get them to compile down as fast as possible into ones and zeros

Going back to the representation above.

If the computer had to open and close the switch 10 times it would be slower where as opening it twice and shutting it twice is much faster 1 open 0 close 1 open 0 close; 4 operations as opposed to 10.

Answer 4

binary number output is 0's and 1's. in decimal number is a whole integer value