# Chapter 1 Binary Systems and Hexadecimal

Chapter 1 and Unit 1.1 and 1.2 consists of:

• ### Conversion of Binary to Denary In Binary Systems, 1 is ON and 0 is OFF. Binary consists of 1 and 0. There many types of Binary such as 8 bit, 10 bit, and 64 bit Binary.  Also there are different things like bases. Base 2 is o and 1, but Base 10 is 0 to 9. you will get this along as we continue.

 128 64 32 16 8 4 2 1 Ans 0 0 1 1 0 0 1 1 51 0 1 1 1 1 1 1 1 127 1 0 0 1 1 0 0 1 153 0 1 1 1 0 1 0 0 116 1 1 1 1 1 1 1 1 255 0 0 0 0 1 1 1 1 15 1 0 0 0 1 1 1 1 143 1 1 1 1 0 0 0 0 240 0 1 1 1 0 0 0 0 128

This is how you transfer numbers from either binary to normal numbers, or the other way around. Each 1 represents the number it is under, and 0 means nothing, so in the end, if you add up everything you get the final outcome.

### Binary to Denary Conversions

Denary is the numbers like 128,64,32,16,8,4,2,1. There are many ways to convert binary to denary. One of the methods is the division method. The way this method works is the division method.  Example we take the number 41. We then divide it by so we get 20.5. Binary doesn’t deal with decimal values, so we can take 20 and put remainder 1, then if we divide 20 by 2, you get 10, a whole number so we can write 0. If you look at the table below, you can see how i have done it.

Then we read the numbers from the bottom and so the answer for 41 is oo1o1oo1

 41 Ans 20 1 10 0 5 0 2 1 1 0 0 1 0 0 0 0

Lets take another example, such as the number such as 86, as you can see, i have divided each number by 2, and the if there is a decimal value, we simply take remainder 1. We then work out everything and then read the numbers from top to bottom. In this case it is                 01011010

 86 43 0 22 1 11 0 5 1 2 1 1 0 0 1 0 0

### Unit 1.3 and 1.4 and 1.5

A binary digit is commonly referred to as a BIT and 8 bits are usually referred to as a byte. The byte is the smallest unit of a memory in a computer or other electronics like a table fan, television remote and things like that. Bytes are always in multiples of 8 such as 8 bit systems, 16 bit systems, 32 bit systems, and stuff like that.

If you look at the numbers, they times it by the number or 2 so its basically the double amount of digits.

 Name of memory size Equivalent denary value 1 Kilobyte 1024 bytes 1 Megabyte 1048576 bytes 1 Gigabyte 1073741824 bytes 1 Terabyte 1099511627776 bytes 1 Petabyte 1125899906842624 bytes

The hexadecimal is quite similar to the binary system, it uses base 16, with all different values.

10000111111101

we split the number in 4 from right to left, so 10 0001 1111 1101

we should add 0010 0001 1111 1101

using the table, its  2 1 F D Hex to denary

Multiply position by value. Hexadecimal converted into denary can have until 5 characters, To work out the value of hex we use the number system below. This method involves successive division by 16. The remainders are then read from the Bottom to Top to give the hexadecimal number

Example 2004

divided by 16 we get 125 with a remainder of 4

again divided by 16, we get 7 remainder 13

then 0 remainder 7

so the outcome from bottom to top will be : 7,13,4 or in Hexadecimal: 7D4

You should look at the first 12 numbers, for the MAC address .  To find your Mac Address go to windows, type “ipconfig” and then press enter. So then you look IPv6 and then look at first 12 numbers in that category.

ASCII

American Standard Code for Information Interchange, ASCII is easier for humans to read and ASCII codes are used to represent web address (URL) . Computers do not understand ASCII, therefore web addresses are programmed using hexadecimal characters as this is an easier to way to represent the destination a website (shorter than binary). Hexadecimal used as a security feature in websites, users who are concerned about website redirects/hackers re pointing URL’s to illegitimate domains can type in the URL using hexadecimal characters, this ensures website address is genuine % is a place holder in HEX for a website, for example www. is %77 %77 %77 %2E

A low level language is either a machine code or an assembly code and python is a high level language.