Assignment 8 Binary!

 Go to this site, its fun:

http://www.nickciske.com/tools/binary.php

Computers work on the principle of number manipulation. Inside the computer, the numbers are represented in bits and bytes. For example, the number three is represented by a byte with bits 0 & 1 set; 00000011. This is numbering system using Base 2. People commonly use a decimal or Base 10 numbering system. What this means is that in Base 10, count from 0 to 9 before adding another digit. The number 22 in Base 10 means we have 2 sets of 10’s and 2 sets of 1’s.

Base 2 is also known as binary since there can only be two values for a specific digit; either a 0 = OFF or a 1 = ON. You cannot have a number represented as 22 in binary notation. The decimal number 22 is represented in binary as 00010110 which by following the below chart breaks down to:

| 2^7 |   2^6 | 2^5  | 2^4 |  2^ 3  |  2^2  |  2^1  | 2^0 |

=         |  128 |   64  |   32  |  16    |    8    |    4    |    2   |    1    |

Computers work on a base of 2 (they understand numbers by powers of 2 eg. 2^2, 2^5…) through 1s and 0s. The number 58 is seen by a computer as 111010

The 1 acts as ON telling the computer to include the number and the 0 acts as OFF.

The computer adds up the numbers that are indicated as ON to determine the number.

As shown above 2^5+2^4+2^3+2^1 which is the same as 32+16+8+2 which equals 58.

Therefore; 58 is 111010 in Binary.

Example:We are given the number 73.

The first step is to subtract the biggest power of 2 equal to or less than 73 in this case being 2^6, 64.

73 – 64 = 9

We know that the first of 7 numbers is now a 1 so we have 1******

The next number we can subtract by is 2^3 which is 8

9 – 8 = 1 therefore we have 1001***

The last number is 1 so we subtract one from one and get 1001001.

1s act as ON and 0s as OFF for each increasing power of 2 from left to right, starting at 2^0.

Conversions:

1 bit

8 bits – 1byte

1024 bytes – 1 kilobyte

1024 kilobytes – 1 megabyte

1024 megabytes – 1 gigabyte

1024 gigapbytes – terrabyte