Objectives

Students will be able to:

  • recognise the use of binary numbers in computer systems
  • convert positive denary (decimal) integers into binary and positive binary integers into denary (to a maximum of 16 bits)
  • show understanding of the concept of a byte and how the byte is used to measure memory size
  • use binary in computer registers for a given application (such as in robotics, digital instruments and counting systems

Intro to Binary (Base 2) Number System


Humans use a number system called decimal (or denary). It uses 10 symbols. It is a base-10 number system.

We can use these numbers in many combinations to represent many different things eg prices in a supermarket or the height of a sky scraper in New York City.

But what about computers? What system do computers use to represent data? Let's find out a little more about it. Complete the worksheet.

Transistors

So what exactly stores these bits of information?

Tiny transistors do this job. These devices, like a light, can only be in one of two states at any given time: on or off.

Humans often think of these states as 1 and 0.

Bytes

A collection of 8 bits is called a byte.

Nibbles

A collection of 4 bits is called a nibble. This is 1/2 a byte!

Binary Counter

   Review

  1. In the decimal system, the first number on the right tells us how many 100 there are; the second number tells us how many 101 there are; the third number tells us how many 102 there are, and so on.
  2. In the binary system, the first number on the right tells us how many 20 there are; the second number tells us how many decimal 21 there are; the third number tells us how many 22 are represented, and so on.
  3. We can use this knowledge to convert from binary to decimal.
  4. Converting from decimal to binary is equally straightforward. eg:

   Task

Let's practice!

Food For Thought

The binary number system uses only ones and zeros. It is a base-2 system because there are only 2 possible states for any one bit of information. Us humans prefer decimal (sometimes called dernary) so it is useful to know how to convery from binary to dernary and vice versa.

convert

25

0

24

0

23

0

22

0

21

0

20

0

SUBSCRIBE

Join my mailing list to receive updates on the latest blog posts and other things.