Two's complement

To allow the possibility of representing negative integers we make use of two's complement.

In this section we will again assume 8-bit registers are being used. Only one minor change to the binary headings needs to be introduced here.

​This left most bit always determines the sign of the binary number

​ 0 0 1 0 0 1 1 1

0 1 0 0 1 0 1 0

​Add 00100111 + 01001010

​ 0 0 1 0 0 1 1 1

0 1 0 0 1 0 1 0

​Add 00100111 + 01001010

Answer: 01110001

​Try the following (from page 16):
a. Convert 126 and 62 into binary.
b. Add the two binary values in part a and check the result matches in the addition of the two denary numbers

​126 in binary

​62 in binary

​a.

​b.

1.1.5 Logical binary shifts

Logical binary shifts

Computers can carry out a logical shift on a sequence of binary numbers. The logical shift means moving the binary number to the left or to the right. Each shift left is equivalent to multiplying the binary number by 2 and each shift right is equivalent to dividing the binary number by 2.

​The denary number 21 is 0 0 0 1 0 1 0 1.
If we put this into an 8-bit register:

If we now shift the bits in this register one place to the left, we obtain:

What do you notice about the denary value of this?

​The denary number 21 is 0 0 0 1 0 1 0 1.
If we put this into an 8-bit register:

If we now shift the bits in this register one place to the left, we obtain:

What do you notice about the denary value of this?

​Try, shifting the above binary number one more place to the left.

This time, use the binary number 1 0 1 0 1 0 0 and shift it three places to the right.

What do you notice now?

1.1.6 Two's complement (binary numbers)

Two's complement

To allow the possibility of representing negative integers we make use of two's complement.
In this section, we will again assume 8-bit registers are being used. Only one minor change to the binary headins needs to be introduced here.

Share with your shoulder partner the method that you used

1.2.1 Character sets - ASCII code and Unicode

The disadvantage of ASCII is that it does not represent characters in non-Western languages, for example Chinese characters. Unicode can represent all languages of the world.

Unicode

ASCII (American Standard Code for Information Interchange) was set up in 1963 for use in communication systems and computer systems. Look up a sample in your textbook, page26

ASCII code

Character Sets

1.2.2 Representation of sound

• Each sound wave has a frequency, wavelength and amplitude.

• Sound waves vary continuously (analogue).

• To convert sound to digital, sound waves need to be sampled (using ADC - Analogue to Digital Converter)

​

• The number of bits per sample is known as sampling resolution.

• Sampling rate is the number of sound samples taken per second.

​

​Read how sampling is used to record a sound clip on page 30 and share with your shoulder partner.
Discuss the benefits and drawbacks of using a larger sampling resolution when recording sound.

1.2.3 Representation of bitmap images

Bitmap images

Bitmap images are made up of pixels (picture elements); an image is made up of a two-dimensional matrix of pixels.

Colour depth

​The number of bits used to represent each colour is called the colour depth.

Image resolution

Image resolution refers to the number of pixels that make up an image; for example, an image could contain 4096 x 3072 pixels.

1.3.1 Measurement of data storage

A bit is the basic unit of all computing memory storage terms and is either 1 or 0.
The word comes from binary digit.
The byte is the smallest unit of memory in a computer. 1 byte is 8 bits.
A 4-bit number is called a nibble - half a byte.

1.3.2 Calculation of file size

1.3.3 Data compression

1.3.4 Lossy and lossless file compression