• 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...

Introduction

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.

Hundredths

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.

Middle

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.

image02.png

32+8+4=44

image03.png

32+16+8+2+1=59

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.

image04.png

...read more.

Conclusion

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.

image07.png

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.

image08.png

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.

    2565 = 20 The difference between the two numbers is 20 4 x 3 boxes 16 17 18 19 X X+1 X+2 X+3 26 27 28 29 X+10 X+11 X+12 X+13 36 37 38 39 X+20 X+21 X+22 X+23 [image001.gif] [image046.gif] 16 x 39 = 624 x (x + 23)

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

    Likewise, if I were using quintets, the factorial to use would be 4 factorial as it is one lower that 5 which is the device being used. Now that I think I have worked out a sequence of formulas which work for any device (trios, quartets, quintets, sextets, septets etc.), I will put it to the test on quintets.

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

    32 + 16+ 8 + 4 + 2 + 1 To get the next term suing the general geometric sequence rule, it says that we have to multiply 32 by a constant. a --> ar. So: a --> ar is the same as ar divided by a. 16 = 0.5.

  1. Investigate calendars, and look for any patterns.

    Ex 1.4 Results for 2001 Months ( n ) Start day 1 Monday 2 Thursday 3 Thursday 4 Sunday 5 Tuesday 6 Friday 7 Sunday 8 Wednesday 9 Saturday 10 Monday 11 Thursday 12 Saturday The matching months are: 1, 10 = same 2, 3, 11 = same 4, 7

  2. About Triangular Square Numbers

    it is beginning to look like 1.4142... = . Now one can apply the first rule: to find p(N7), Now one can apply the second rule to see if it yields the same result: Voila! The same result. Since the index, 7, is odd, it follows that t(N7)

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