Site Logo Home
 
rOm
Quest
Glossary
 
Random
Page
Search
Site
Lush
Sim
Class
Subject
Images
 
Help
FAQ
Sign
Up
Log
In
AS Level     >Basics Binary and Hex<    

Basics Binary and Hex


Site for Eduqas/WJEC - Go to the AQA site.

  AS Level    Binary and Hexadecimal  0 of 9    Question 1085    Bits, Bytes and Nybbles 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set1 of 9    Question 1007    Bits, Bytes and Nybbles 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set2 of 9    Question 1008    Bits, Bytes and Nybbles 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set3 of 9    Question 535    Convert Binary to Decimal 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set4 of 9    Question 913    Convert Binary to Hexadecimal 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set5 of 9    Question 420    Convert Binary to Hexadecimal 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set6 of 9    Question 423    Convert Binary to Hexadecimal 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set7 of 9    Question 424    Convert Binary to Hexadecimal 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set8 of 9    Question 418    Convert Decimal into Binary 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set9 of 9    Question 419    Convert Hexadecimal into Binary 
Score 0/0 
Not attempted  
Last Answer  
Deadline not set  Questions 0 to 9   -->  View All  

Binary is the base 2 number system counting 0, 1, 10, 11, 100, 101, 110, 111, 1000, etc.

Binary Su doku    Thanks xkcd

Decimal and Binary - Everyone

Decimal Numbers

These are used in everyday life and are so familiar that many important features get forgotten.

Binary Numbers

Binary Bit

One binary digit. A zero or a one.

Byte

A group of eight bits. Computer data is usually stored and processed in bytes or pairs of bytes or even groups of four or eight bytes.

Nybble

This is half a byte or four bits. The word was originally a joke but the term proved useful.

In an eight bit byte such as 11100111, the HIGH nybble is 1110 and the LOW nybble is 0111.
They are called low and high because the low nybble is worth 0 to 15 in decimal numbers and the high nybble allows numbers up to 255.

Nybble is often spelled nibble. Internet flame wars rage over this!

Word

Grouped bytes are called words. 64 bit computers common in 2015 work with 8 byte groups. 8 x 8 = 64 bits in the word.

LSB and MSB

In this number: 11100111 the

Getting bits back to front causes serious errors so it's important to pay attention to this.
This mistake crops up frequently when designing binary counters to reset on specific numbers like ten.

Decimal Binary Conversion

        Decimal                 Binary        
  8 4 2 1
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
10 1 0 1 0
11 1 0 1 1
12 1 1 0 0
13 1 1 0 1
14 1 1 1 0
15 1 1 1 1

Converting Larger Numbers

Decimal         128                 64                 32                 16                 8                 4                 2                 1          
Binary 0 0 1 1 0 0 0 1  
Yes/No 0 0 32 16 0 0 0 1 Total = 49

Little and Big Endian

A 64 bit computer could put the most significant byte at the left or right end of the group of eight bytes. Different computer manufacturers use both schemes. This makes it more difficult to store and transfer data between incompatible systems. Data munging is needed to reverse the byte order. Internet flame wars rage over this topic.

Hexadecimal Numbers

Uses of Each System

Binary Hexadecimal Conversion

It does not take long to jot down this table. Then you can just look up the binary/hexadecimal conversions

        Decimal                 Binary        
  8 4 2 1
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
A 1 0 1 0
B 1 0 1 1
C 1 1 0 0
D 1 1 0 1
E 1 1 1 0
F 1 1 1 1

Converting Bigger Numbers

        0011                 0010                 1001                 1100        
3 2 9 C

Here are some examples of hexadecimal numbers ...

0x3F9C This notation is used by AQA, Microsoft Windows, C, C++, C# and Java programmers.
&H3F9C This notation is used by BASIC programmers
$3F9C This notation is used by Pascal programmers
3F9C16 This is how hexadecimal numbers are written in printed text.

Problems Solved Using 2N or 2N - 1

What is the biggest number that can be stored in a six bit memory location? 26 - 1 = 63
If each pixel uses 24 bits to store the colour, how many colours are there? 224 = 16.7 Million
A computer has a 20 bit address bus. How many addresses can it access? 220 = 1 Million
A digital to analogue converter uses 8 bits. How many levels are available for the digitised signal? 28 = 256
A microcontroller has a 14 bit word. 8 bits are used for data and six for instruction op-codes. How many op-codes could be available? 26 = 64
How many colours are available if four but colour is being used? 24 = 16
What is the biggest number that can be stored in a four bit latch? 24 - 1 = 15
Monochrome displays use black and white. How many bits are needed to store each pixel? 21 = 2 so only one bit is needed.

 

Subject Name     Level     Topic Name     Question Heading     First Name Last Name Class ID     User ID    

fff
Home
<<<
ppw
Pg Up
<<
ppp
Up
<
|||

>|<
nnn
Down
>
nnw
Pg Down
>>
lll
End
>>>

Close
Escape
X

Q: qNum of last_q     Q ID: Question ID         Score: num correct/num attempts         Date Done    

 

Submit
Enter

 

Question Text

image url

 


Help Link

Add     Delete     Clone     Edit     Hardness

Help Text
Debug


 

 

 

Contact, Copyright, Cookies and Legalities: C Neil Bauers - reviseOmatic V4 - © 2016/17

Hosted at linode.com - London