How do you convert binary number 10011110 to a decimal number?

Answer 1

Starting with the rightmost, multiply each binary digit by an increasing power of two, and add the results. Like this:

0 x 1 = 0

1 x 2 = 2

1 x 4 = 4

1 x 8 = 8

1 x 16 = 16

0 x 32 = 0

0 x 64 = 0

1 x 128 = 128

total = 158

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158.

In binary there are only 2 digits, 0 & 1. Each digit working from right to left is a multiple of a power of 2 (starting at 0), with the power increasing by 1 as we move a digit to the left (this is the same principle as in decimal, except in decimal there are 10 digits and each digit is a multiple of a power of 10).

So, in binary this number actually means (working from right to left):

(0 * 20) + (1 * 21) + (1 * 22) + (1 * 23) + (1 * 24) + (0 * 25) + (0 * 26) + (1 * 27)

which equals 0 + 2 + 4 + 8 + 16 + 0 + 0 + 128

which equals 158 (one hundred and fifty eight) in decimal.