Computer Logic Chapter 2

                    

COMPUTER LOGIC CHAPTER 2

·         2-STATE DEVICES ( BISTABLE DEVICES)

A two-state device is like a switch on a wall, it can be in only one of two possible states at any given time eg. it may be either ON or OFF

Another example is a light bulb wich it may be either :

 

 illuminated bulb [ switched on]      Not illuminated bulb [ switched off ]

 

— What are computer made of ?

Computer systems are not built from light switches, but they have been built using a wide range of devices. Today the elementary building block for all modern computer systems is the TRANSISTOR [ is much like the light switch ,it can be in a OFF state which doesn’t allow electricity to flow or a ON state which let electricity to flow fleerly. The switching of a transistor is done electronically rather than mechanically. This allow it to be fast as well as extremely small.

 

— What’s binary ?

Computer people, however, do not like talking about the prescence or absence of electrical charges. They prefer to represent this using binary.

NOTE : binary is a number system. Its is the ideal number system to represent two-states because it was only two digits 0 and 1. It is important to notice that the number system we use in everyday life called the decimal number system, ten digits is used : 0 1 2 3 4 5 6 7 8 9 .

Binary then with it's 0s and 1s, is very convenient method of represending the two internal states of a computer's electronic components eg. +5 volts can be represented by binary 1 and the abcene of charge (zera volts) by binary 0.

Definition: A bit (binary digit) is a single digit from a binary number. It is eight a 0 or a 1.

— Using Many Bits :

The more bits we use to represent an item of data, the more different values we can represent. As an example, we will consider 3 bulbs, and write down the different combinations in which they can be, using 1 to represent a bulb which is ON on O to represent a blub which is OFF.

 

Bulb 3                  Bulb 2                     Bulb 1

0                           0                              0

0                           0                              1

0                           1                              0

0                           1                              1

1                           0                              0

1                           0                              1

1                           1                              0

1                           0                              1

Every 4 ^            Every 2 ^                   Every 1 ^

 

NOTE : with 3 bits you can have 8 different values

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BULB 4	BULB 3	BULB 2	BULB 1
0	0	0	0
0	0	0	1
0	0	1	0
0	0	1	1
0	1	0	0
0	1	0	1
0	1	1	0
0	1	1	1
1	0	0	0
1	0	0	1
1	0	1	0
1	0	1	1
1	1	0	0
1	1	0	1
1	1	1	0
1	1	1	1

 

           


                                      

                                   





                                   





















                                       Bulb 4 = every 8 = 2⁴=16

                                       Bulb 3 = every 4 = 2³= 8

                                      Bulb 2 = every 2 = 2²⁼  4

                                      Bulb 1 = every 1 = 2¹= 2  

NUMBER OF BITS	DIFFERENT VALUES
1	21= 2
2	22=4
3	23=8
4	24=16
5	25=32
6	26=64
7	27=128
n	2n

               Note : in general we can represent 2ⁿ for different values

Rangers :

— With 1 bit we can only represent 2 numbers : 0,1

— With 2 bits we can represent 4 numbers. Hence starting from 0, the largest number that can be represented is 3. Hence the range of decimal numbers that can be represented is 0…3

2nd  bit	1st  bit	Representation decimal
0	0	0
0	1	1
1	0	2
1	1	3

— With 3 bits we can represent 8 numbers. Hence the range of decimal numbers that can be represented is 0…7

Formula : 2ⁿ-1. Hence the range of decimal numbers that can be represented is 0…2ⁿ…1

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Here are the basics binary coveration binary to decimal. Hope you enjoy :)

 

 

— Number conversions

Number in decimal are said to be base 10 whilst numbers in binary are said to be base 2. In our decimal number system, every digit has a place value in a power of 10.

103	102	101	100
Thousand	Hundred	Tens	Units
8	4	2	5

 

NOTE: in the binary number system, every bit has a different value always multiplied by 2 as the bits increment.

Example : 1101011₂

26	25	24	23	22	21	20
64	32	16	8	4	2	1
1	1	0	1	0	1	1

 

— The bit with the smallest value: Least Significant Bit (LSB)

— The bit with the largest value : Most Significant Bits (MSB)

— A hexadecimal number is a short way of writing a binary number. Hexadecimal numbers system are said to be base 16 because it has 16 digits : 1,2,3,4,5,6,7,8,9, 10-A ,11-B , 12-C ,13-D , 14-E , 15-F , 16-G a binary number can be directly transferred to hexadecimal numbers by grouping the bits in packets of four, starting from the LSB , then each packet is given the weights 1,2,4,8 etc. to convert it into hex digit.

— Representation of Characters

Besides numbers , characters are also used in everyday life to express information. This means that characters also have to be represented in binary using a unique binary code. This is called the character code

If 8 bits is used to store a character, 256 characters can be stored (2⁸=256)

— ASCII:

American Standard Code for Information Interchange is an 8-bit code used to represent characters in binary.

Eg. The character A would be represented as 0100001₂ (65₁₀)

— Units of storage:

In order to represent numbers, letters and special characters, bits are combined into groups of 8 bits called bytes. Each byte typically represents one character- in many computers, one addressable storage location.

Unicode:

— While the ASCII system is widely accepted and used in computer industry, it has a number of major limitations.  

— Unicode by using 16 bits to represent each character. These 16 bit binary allow 2¹⁶ different combinations to be represented which can add up to 65,536 different characters.

Binary Notations  

— A BIT can be either 0 or 1

— A Byte is made up of 8 bits

— 1 KILOBYTE = 1024 bytes  1000 bytes

— 1 MEGABYTE is 1024 kilobytes  1000 x 1000 x 1000 bytes

— 1 GIGABYTE  is 1024 megabytes 1000 x 1000 x 1000 bytes

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sorry its a bit long but its a really important chapter so i hope it helped you :)