Analog and Digital Signals
The Binary Number System
The basic numbers that we learned in elementary school are called decimal numbers. However, computers communicate in a different language and use numbers called binary numbers.
Binary numbers are a series of zeros and ones. In order to understand the binary number system, a conversion has to occur to translate binary numbers to decimal numbers.
Binary numbers are a series of zeros and ones. In order to understand the binary number system, a conversion has to occur to translate binary numbers to decimal numbers.
The Conversion:
![Picture](/uploads/3/7/8/6/37860027/1431531999.png)
To convert a decimal number to a binary number there are two steps that are just repeated until you have found the complete binary number.
Step 1: Divide the decimal number by two
Step 2: If there is a remainder, the first number of your binary number is 1. If there is no remainder, the first number of your binary number is 0.
Now repeat the steps using the remaining whole number.
Example.
Convert the decimal number, 6, into its binary equivalent
The answer is 011.
Step 1: Divide the decimal number by two
Step 2: If there is a remainder, the first number of your binary number is 1. If there is no remainder, the first number of your binary number is 0.
Now repeat the steps using the remaining whole number.
Example.
Convert the decimal number, 6, into its binary equivalent
The answer is 011.
Octal and Hexadecimal Number Systems
Since computers have 32, 64, and even 128 bit buses, displaying numbers in binary can be unmanageable. Hexadecimal and Octal number systems are used to represent binary data in am ore compact and manageable form.
The Conversion
![Picture](/uploads/3/7/8/6/37860027/1431641691.png)
The conversion from decimal numbers to octal and hexadecimal numbers is the same as the conversion from decimal to binary. The process itself is called successive division. The steps are the same, the only difference is that instead of dividing by 2, you divide by 8 for octal numbers and by 16 for hexadecimal numbers.
Example.
Convert the decimal number, 94, into its octal equivalent.
The answer is 136.
Example.
Convert the decimal number, 94, into its octal equivalent.
The answer is 136.
![Picture](/uploads/3/7/8/6/37860027/1431642127.png)
Example.
Convert the decimal number, 94, into its hexadecimal equivalent.
The answer is 5E.
Convert the decimal number, 94, into its hexadecimal equivalent.
The answer is 5E.
Scientific and Engineering Notation
Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10^-9
Engineering notation is a version of scientific notation in which the powers of ten must be multiples of three. For example, 1000^2 would instead be written as 10^6.
Engineering notation is a version of scientific notation in which the powers of ten must be multiples of three. For example, 1000^2 would instead be written as 10^6.
Two's Complement Arithmetic
This arithmetic helps solve the two zero's problem (000 and 111) in a 3-bit system. To do this, complete the following steps: Flip each number in the binary, Add 001, This ensures that you get the same answer while understand what value you originally had for binary