 Different number systems are used by digital circuitry to perform various functions. Some number systems are used to display numerical values. Other number systems are used as a shorthand method for programming, and binary numbers are processed by the internal circuitry of digital devices. To know how some digital circuits operate, it is necessary to understand the number systems used by them and how to make conversions from one to another. In this lesson, a method used to convert from decimal numbers to equivalent binary values will be presented. The number system that we are familiar with is the decimal number system. It uses 10 digits. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is a place value system where the value of each digit depends on its position in the number. We can write the decimal number 6,736 in expanded form. Notice that the leftmost 6 represents 6,000s. And the rightmost 6 represents 6,1s. Since we multiply each digit by a power of 10, we often call the decimal system a base 10 number system. The binary number system is a base 2 number system. It uses two digits, 0 and 1. In this learning activity, you will examine a method that converts a decimal number to a binary number. Subscripts are used to help us identify what type of number is given. Note how the binary number 10111 can be written in expanded form. Since each digit is multiplied by a power of 2, we call the binary number system a base 2 number system. Let's examine an algorithm for converting a decimal number to a binary number. Convert the decimal base 10 number 29 to its equivalent binary or base 2 number. The algorithm involves repeated divisions. Since we are converting from a decimal number to a binary number, we will do repeated divisions by 2. Start with the given decimal number. Divide 2 into 29. Notice the upside down division symbol. If we divide 2 into 29, we get a quotient of 14 with a remainder of 1. Note the placement of the remainder. Now divide 2 into 14. If we divide 2 into 14, we get a quotient of 7 with a remainder of 0. Note the placement of the remainder. Now divide 2 into 7. If we divide 2 into 7, we get a quotient of 3 with a remainder of 1. Once again, note the placement of the remainder. Now divide 2 into 3. If we divide 2 into 3, we get a quotient of 1 with a remainder of 1. Note the placement of the remainder. Once we get a quotient of 0, the division process is complete. The binary equivalent of decimal 29 is obtained by using the remainders in the right column. We write the binary equivalent by starting at the bottom of the remainder column and working up. Decimal 29 is equivalent to binary 11101. Let's work through one more example of converting a decimal number to a binary number. Convert the decimal or base 10 number 324 to its equivalent binary or base 2 number. Start with the given decimal number. Divide 2 into 324. If we divide 2 into 324, we get a quotient of 162 with a remainder of zero. Now divide 2 into 162. If we divide 2 into 162, we get a quotient of 81 with a remainder of zero. Now divide 2 into 81. If we divide 2 into 81, we get a quotient of 40 with a remainder of one. Now divide 2 into 40. If we divide 2 into 40, we get a quotient of 20 with a remainder of zero. We repeat these steps until we get a quotient of zero. The binary equivalent of decimal 324 is obtained by using the remainders in the right column. We write the binary equivalent by starting at the bottom of the remainder column and working up. Decimal 324 is equivalent to binary 1 0 1 0 0 0 1 0 0. Congratulations! You have learned how to convert decimal numbers to binary numbers. This knowledge is necessary to understand how the internal circuits of digital devices make these conversions and how to troubleshoot the circuits if the devices become defective.