 The Numeric Systems

 Introduction
 The Binary System
 When dealing with assignments, the computer considers a piece of information to be true or to be false. To evaluate such a piece, it uses two symbols: 0 and 1. When a piece of information is true, the computer gives it a value of 1; otherwise, its value is 0. Therefore, the system that the computer recognizes and uses is made of two symbols: 0 and 1. As the information in your computer is greater than a simple piece, the computer combines 0s and 1s to produce all sorts of numbers. Examples of such numbers are 1, 100, 1011, or 1101111011. Therefore, because this technique uses only two symbols, it is called the binary system. When reading a binary number such as 1101, you should not pronounce "One Thousand One Hundred And 1", because such a reading is not accurate. Instead, you should pronounce 1 as One and 0 as zero or o. 1101 should be pronounced One One Zero One, or One One o One. The sequence of the symbols of the binary system depends on the number that needs to be represented. Why learn the binary system? You need to know what the binary system looks like because you will be writing instructions to the computer, and the computer does not understand English.

 The Decimal System

The numeric system that we have always used uses a set of ten symbols that are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each of these symbols is called a digit. Using a combination of these digits, you can display numeric values of any kind, such as 240, 3826 or 234523. This system of representing numeric values is called the decimal system because it is based on 10 digits.

When a number starts with 0, a calculator or a computer ignores the 0. Consequently, 0248 is the same as 248; 030426 is the same as 30426.

From now on, we will represent a numeric value in the decimal system without starting with 0: this will reduce, if not eliminate, any confusion.
Decimal Values: 3849, 279, 917293, 39473
Non- Decimal Values: 0237, 0276382, k2783, R3273

The decimal system is said to use a base 10. This allows you to recognize and be able to read any number. The system works in increments of 0, 10, 100, 1000, 10000, and up.

In the decimal system, 0 is 0*100 (= 0*1, which is 0); 1 is 1*100 (=1*1, which is 1); 2 is 2*100 (=2*1, which is 2), and 9 is 9*100 (= 9*1, which is 9). Between 10 and 99, a number is represented by left-digit * 101 + right-digit * 100. For example, 32 = 3*101 + 2*100 = 3*10 + 2*1 = 30 + 2 = 32. In the same way, 85 = 8*101 + 5*100 = 8*10 + 5*1 = 80 + 5 = 85. Using the same logic, you can get any number in the decimal system. Examples are:

2751 = 2*103 + 7*102 + 5*101 + 1*100
= 2*1000 + 7*100 + 5*10 + 1 = 2000 + 700 + 50 + 1 = 2751

67048 = 6*104 + 7*103 + 0*102 + 4*101 + 8*100
= 6*10000 + 7*1000+0*100+4*10+8*1 = 67048

Another way you can represent this is by using the following table:

 etc Add 0 to the preceding value 1000000 100000 10000 1000 100 10 0

When these numbers get large, they become difficult to read; an example is 279174394327. To make this easier to read, you can separate each thousand fraction with a comma. Our number would become 279,174,394,327. You can do this only on paper, never in a program: the compiler would not understand the comma(s).

Why use the decimal system? Because, to represent numbers, that is the system that you and I are familiar with.