• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Binary Explained.

Extracts from this document...


Binary Explained

Before we can talk about Binary numbers, I need to explain Decimal numbers. Decimal numbers are also known as denary numbers and Base ten. Ten is the bases of decimal numbers simply because we are used to using our fingers to count. By adding a place value determines the meaning of the number, for instance, 192 is a smaller number than 219 although the same numbers have been used. To produce a number in decimal we use one of the ten digits. These are:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

Below is a table to show how the decimal 235 is made up.


Binary numbers work in a different way, they use a base number of two and so they only use two symbols, 1 and 0. Below is a table to explain how the decimal equivalent would be written.

This is how binary works.

...read more.


Table 2

We see that 32, 8 and 4 have the number one under them so we add these numbers to the total.

32 + 8 + 4 = 44 (in Decimal form)

By following table 1, we can start converting the binary numbers to produce decimal numbers here are two examples.





The same process is used to produce smaller numbers as well. Zero may be shown as 0 in all the columns.

To convert back to binary we use repeated division of 2. The number I will convert back to binary will be 54. A common problem with converting back to binary is that a lot of people convert it right, but they don’t put the numbers in the right order. So what we say is, the first division number goes to the right, and then the next number goes next to it on the left, and so on. I will show how the conversion is done below.


...read more.


Hexadecimal Coding has a base of 16, and the symbols used are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F. The symbols A, B, C, D and F are representing the numbers 10, 11,12,13,14 and 15 in decimal form. Where as octal has groups of 3 bits, hex has groups of 4 bits. This is where the letters are used. Since we know how the lower numbers are used I will show below how the symbols 9 and above work.


Now that the groups have four bits to it, we can code binary into hex, by splitting up the binary into groups then working out the symbol. An example is shown below.


Hexadecimal is used more than octal because computers organise their internal memory in 8-bit groupings or bytes and also multiples of bytes. These grouping can be divided into 4-bit nibbles, which can be coded as a short hand of hex.

...read more.

This student written piece of work is one of many that can be found in our GCSE Consecutive Numbers section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Consecutive Numbers essays

  1. GCSE Maths Coursework - Maxi Product

    I have found that 4 1/3, 4 1/3, and 4 1/3 are the three numbers which added together make 13 and when multiplied together make 81.370 (3dp) which is the highest possible answer which can be retrieved when three numbers added together equal 13 are multiplied.

  2. Investigate the Maxi Product of numbers

    I have found that 7.5 and 7.5 are the two numbers which added together make 15 and when multiplied together make 56.25 which is the highest possible answer which is retrieved when two numbers added together equal 15 are multiplyed.

  1. In this investigation I will explore the relationship between a series of straight, non-parallel, ...

    = 20 2 CR (6) = 10 CORRECT! I predict: CR(7) using the formula CR(n) = (n2 -3n + 2) 2 [where (n) is the number of lines in the diagram] let n = 7 CR(7) = (72 -3(7) + 2) 2 CR(7) = 49 -21 + 2 2 CR(7)

  2. I am to conduct an investigation involving a number grid.

    23 24 32 33 34 [image045.gif] 22 x 34 = 748 32 x 24 = 768 768 - 748 = 20 The difference between the two numbers is 20 Box 3 45 46 47 55 56 57 [image025.gif] 45 x 57 = 2565 55 x 47 = 2585 2585 -

  1. Study the topic of trios and work on from that, to discover patterns and ...

    QUINTETS: I do not need to investigate all the numbers with quintets as I have done with trios and quartets as I believe that I already have the formula. I must, however, check using one number (I choose 6) in order to make sure that the formula I have created actually works.

  2. The Towers of Hanoi is an ancient mathematical game. The aim of this coursework ...

    This gave: S-rS = a - arn = a(1-rn) Therefore S=a(1-rn) (1-r)) Limitations are: S has to be greater than 0 and has to be an integer a has to be positive and an integer r has to be an integer and greater than 0 Extension Work: Finding which pole the pile will be built upon.

  1. Investigate calendars, and look for any patterns.

    = same 5 7 8 9, 12 = same As you can see, once again the results for the months that start on the same day show the same pattern as in Ex1.1 and Ex1.3. This clearly shows that there is indeed a pattern between the start days of the months each non - leap year.

  2. About Triangular Square Numbers

    = p2(N7) = 2392 = 57121. So N7 is the 57121th triangular number, viz. , and , so N7 = 1631432881 is the 40391th perfect square, and it is the seventh triangular square. Repeating the paradigm shown above, it can be found that the eighth triangular square is: N8 =

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work