 Various numbering systems use symbols to refer to a number of items. Our common decimal system uses 10 numeric symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, sometimes called the base 10 system. We use this system to write numbers and perform mathematical operations. The position of a digit in the base 10 system determines its magnitude. This is referred to as place value. Moving from right to left, we multiply each preceding digit position by 10. Therefore, starting from the right, the first digit position is 1. The second digit position is 10 times the first or 10. The third digit position is 10 times the second or 100, and so on. The magnitude of the numbers 6, 9, and 4 is determined by the position of the digits. With the 6 in the third position, we would multiply 6 by 100 to derive its place value of 600, then add to it 9 times 10 or 90, and to that 4 times 1 to get 694. The binary system also uses place value to determine the magnitude of a number, but uses only 0 and 1 as numeric symbols. Thus, it is referred to as the base 2 system with each position incremented by a multiple of 2. Digital systems use the base 2 system for computational operations in many of its applications. Now, let's consider place value in the base 2 system. Starting at the right, we have 2 to the zero power, then 2 to the first power, then 2 to the second power, and so on. Thus, each multiplier to the left is 2 times the preceding number. Thus, starting with position 1, we have 2 to the zero power or 1, position 2 is 2 to the first power or 2, position 3 is 2 to the second power or 4, and so on. When you work with digital equipment, converting between the binary and decimal numbering systems is often required. Let's take the binary number 1, 1, 0, 1, 0, 1, and convert it to a decimal number equivalent. We will add together all the decimal number place values converted from a binary string. Thus, moving from right to left, we encounter a 1. Multiply it by its binary place value of 1 to give 1. Considering the next position to the left, we have a zero. No decimal numbers are derived when zeros are encountered because zero times its multiplier is zero. The next binary number is 1. 1 times 4 is 4, so we include its place value of 4. We do this conversion for each place value of the binary number. Thus, adding up all the decimal numbers gives 53. Now, let's apply a process for converting a decimal number to its binary equivalent. This method involves repeated divisions by 2. Taking the base 10, number 37, and dividing by 2, we get a quotient of 18 with a remainder of 1. This remainder occupies the first position. Next, you'll divide 18 by 2 to get the next digit. It will be 9 with a remainder of 0, so 0 will occupy the second position. Moving along, the third position will be determined by dividing 9 by 2. This will give you 4 with a remainder of 1 to occupy the third position. Applying this divide by 2 process to each new calculated quotient derives the remainders that become the zeros or ones used to create the binary string. Continuing until the quotient is 0 and can no longer be divided by 2 completes the conversion process and you have your binary number.