Tips & Tricks

# Digital Numbering Systems

Digital information has been used by human beings during almost all of their history. Parts of the human body were first used as a means of counting. Fingers and toes were often used to represent numbers. In fact, the word digitus in Latin means finger or toe. This term is the basis of the word digital.

Most counting that we do today is based on groups of 10. This is probably an outgrowth of our dependence on fingers and toes as a counting tool. Counting with Was a base is called the decimal system. Ten unique symbols, or digits, are included in this system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In general, the number of discrete values or symbols in a counting system is called the base, or radix. A decimal system has a base of 10.

Nearly all numbering systems have place value. This refers to the value that a digit has with respect to its location in the number. The largest number of value that can be represented at a specific location is determined by the base of the system. In the decimal system, the first position to the left of the decimal point is called the units place. Any number from 0 to 9 can be used in this place. Number values greater than 9 are expressed by using two or more places. The next location to the left of the units places in the 10s position. Two-place numbers range from 10 through 99. Each succeeding place added to the left has a value that is 10 times as much as the preceding place. With three places, the place value of the third digit is 10 x 10 x 10, or 1000. For four places, the place value is 10 x 10 x 10 x 10, or 10,000. The values continue for 100,000, 1,000,000, 10,000,000 and so on.

Any number in standard form can be expressed in expanded form by adding each weighted place value. The decimal number 2319 is expressed as (1000 x 2) + (100 x 3) + (10 x 1) + (1 x 9). Note that the weight of each digit increased by 10 for each place to the left of the decimal point. In a number system, place values can also be expressed as a power of the base. For the decimal system, the place values are 10°, 101, 102, 103, and so on. Each succeeding place has a value that is the next higher power of the base.