Binary code can be translated into decimal values, keyboard characters or computer processor instructions through the multiplication of the ones and zeros in the bit string by the number two taken to the power of the place-value of the one or zero being manipulated. These multiplications are then added together.
Binary code is read from right to left. The first place-value of the sequence is zero, the second is one, and so on. As a base two numerical system, the ones and zeros of the bit string are thus multiplied by two. As an example, if the far right digit in a bit string is a zero, and the following digit to the left is a one, the value of the pair is calculated by multiplying the zero by two taken to the power of zero, and adding that product to the product that results from multiplying the one by two taken to the power of the second place-value, which is one. The sum is thus zero plus two, or the decimal value two.
One other method of deciphering binary bit strings is to assign place-values from right to left, beginning at one, and doubling the place-value with each place moved to the left. The first place-value is thus one, the second is two, the third is four, and so on. The value of the binary expression is determined by adding together the place-values that correspond to the ones of the string only. For example, when binary string "101" is translated by this method, the first place-value is added only to the third, because the second corresponds to a zero. Thus, the decimal value equals five.