calculating binary to decimal manually?

Answer 1

Here is a demonstration with 1 byte (256 possibilities: 0-255):

The value of each bit (from right to left) is base^position with positions starting at 0. So it goes:

position: 7 6 5 4 3 2 1 0
value: 128 64 32 16 8 4 2 1

binary: 0 1 1 0 1 0 1 0
then equals (still reading from right to left):
2+8+32+64=106

Answer 2

Converting Binary to Decimal Manually

Information stored in computers is stored as bits. Each bit is a basic unit
of information having a value of 1 or 0.

Bits are grouped into units of 8 and are called bytes.

Lets examine a group of 8 bits. Each bit has a state value of 0 or 1.
Starting from right to left each bit has a positional value of 1, 2, 4, 8,
16, 32, 64, 128 and so forth. When the state value of the bit is 0 the
positional value of the bit is 0. When the state value of the bit is 1 the
positional value of the bit is equal to its positional value shown below:

1
2 6 3 1
8 4 2 6 8 4 2 1

0 0 0 0 0 0 0 0

Each position moved to the left doubles in value from the preceeding
bit position.

With this knowledge we can calulate the decimal value of any binary
number manually like this.

E.g. Convert 10101010 to decimal.

128+32+8+2=170

http://www.wikihow.com/Convert-from-Binary-to-Decimal

Answer 3

Each part of the binary numbers are bits. For example this string of binary numbers has 4 bits.
0000

Now to convert binary into decimal you have to start from right and read left...for example.

If the binary string is 0000. You would begin counting from the farthest right bit and work towards the left.

Each bit in the binary string is in 2's. For example the far right bit is 1, the next 2, the next 4, the next 8, and so on. The numbers double each bit you move to the left.

To convert a binary number to a decimal, all you have to do is add. For example, if the binary string is 0000. Then the decimal number is 0.
If the string is 0001. Then we add the bit(s) that have a 1 in them. We know that the far right bit is decimal 1. So this binary string equals 1 in decimal.

Now lets try 0101. We only count the bits with a 1 in them. The far right bit has a one and is equal to 1. The third bit from the right has a one in it, so we count from right to left...1, 2, 4. We now know that both bits that have a 1 in them are equal to 1 and 4. Now we add those numbers to get decimal 5. So the binary string of 0101 is equal to the decimal 5.

There you go, hope that helps.

Answer 4

Its simple.

Basically each bit represents a value interms of 2^x .

so if you have

0 1 1 0 => we know it is 6
| ---- |
msb lsb
the procedure of doing it is

starting from lsb (Least significant bit)

issue numbers from 0, 1, 2, 3 till msb (most significant bit)

thus we get

0 1 1 0
3 2 1 0

now raise these numbers to the power of 2

i.e

2^3 2^2 2^1 2^0

their corresponding bits are 0 1 1 0

so my\ultiply the corresponding bits to the 2^x & add it to find teh sequence.

0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^ 0

= 0 + 4 + 2 + 0 = 6

that is how you can calculate the binary to decimal

Answer 5

Start from the leftmost bit, and set the value to be 1.

Then for each subsequent bit in strict sequence:
1) double the value
2) add the bit to the value

So 10110001 converts to decimal in the following sequence :-

1; 2; 4, 5; 10, 11; 22; 44; 88; 176, 177.

Answer 6

Julie has the best answer. It's just a base 2 to base 10 conversion.