This idea and some of the questions that follow are based on the concept material in the manual for Computer Science Course 103, © The University of Waikato , 2003 by Professor Ian H Whitten and others .

Since "the others" include me and "they" are still using "my" notes for the course I don't feel too bad about this :-)

On this page: [ binary | negative numbers | characters | pictures | units of bits/bytes ]

This Applet simulates the physical card deck we use in our lessons. The Applet source code is here. If you have trouble seeing the Applet, download the free jre from http://www.java.sun.com or use the Flash Version (requires Flash Player)..

Make the sequence 0 1 1 0 1. The zero represents the card when it is face down and therefore whether the value of the card is to be counted. Therefore the binary number 01101 is equivalent to the decimal number 13.

Back to top

Binary
We have used 5 cards here; normally binary bits are grouped in sets of 8 called a byte:

The above represents decimal 22. Notice that by convention we usually show the leading zeroes in a binary number (although we don't usually write 000022 for decimals).

Back to top

Negative numbers
How can negative numbers be represented? As it turns out there are many ways but probably the two most popular are sign and magnitude and two's complement.

Two's Complement
In this system the most significant bit (on the far left) is the same value as normal but negative:

One advantage of this system is that we can subtract binary numbers by adding a negative one to a positive one. This is quite easily done with electronic circuitry.

Back to top

Characters
So far we've seen how numbers can be stored in the computer but character data is important to - otherwise we could not type in text or see writing on the monitor.

Characters are often represented using ASCII (American Standard Code for Information Interchange). In this system, every character (even some that don't print) has its own binary code:

Back to top

Pictures
We are used to the idea of computer graphics. How can a picture be stored in 1's and 0's? A picture in the computer is composed of small elements called pixels, these are square or rectangular and each one can hold only one colour.

If we only want to represent two colours (black and white, say) we need only 1 bit per pixel:

         0 0 0 0 0 0 0 0
         0 0 0 1 1 0 0 0
         0 0 1 1 1 1 0 0
         0 0 1 1 0 1 0 0
         0 0 1 1 0 0 0 0
         0 0 1 1 1 1 0 0
         0 0 0 1 1 1 0 0
         0 0 0 0 0 0 0 0

Back to top

Measuring Computer Memory
The term bit refers to the individual 1 or 0, denoted by the symbol of the single letter b.

The term byte refers to the standard grouping of 8bits into a single unit denoted by the single letter capital B .

Thus 4 Mb of memory is very different to 4 MB of memory.

In the decimal system, we often see the following measurements used:

Tera (T) 1,000,000,000,000
Giga (G) 100,000,000
Mega (M) 1,000,000
kilo (k) 1,000

In computing the measurements such as K are slightly different to those shown above in the table since the computer operates on the binary system.

For example 1 KB = 1024 (2 10 ) bytes; often we use the term KB as an approximation for 1000
bytes. Strictly speaking, the following terms are defined for computer memory.

Tera (T) 240
Giga (G) 230
Mega (M) 220
kilo (k) 210

Back to top

related: [ Core home | previous: languages | next: number systems ]

Here is a link to the worksheet (pdf) we use with the cards.

Here is the same thing in Flash (in case of Applet trouble); opens in a new browser window.

Questions or problems related to this web site should be addressed to Richard Jones who asserts his right to be identified as the author and owner of these materials - unless otherwise indicated. Please feel free to use the material presented here and to create links to it for non-commercial purposes; an acknowledgement of the source is required by the Creative Commons licence. Use of materials from this site is conditional upon your having read the additional terms of use on the about page and the Creative Commons Licence. View privacy policy.