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Inside Chip Computing ?

 

 

 

 

 

 

( The 4004 was released on November 15, 1971 . was the first commercially available computer processor designed and manufactured by chip maker Intel.The chief designers of the chip were Federico Faggin and Ted Hoff of Intel, and Masatoshi Shima of Busicom )

Data Formats

1. Binary

Binary pertains to a number system that has just two unique digits. For most purposes we use the decimal number system, which has ten unique digits, 0 through 9. All other numbers are then formed by combining these 10 digits. Computers are based on the binary numbering system, which consist of just two unique numbers 0 and 1. All operations that are possible in the decimal system ( addition, subtraction, multiplication, division ) are equally possible in the binary system.

We use the decimal system in every day life because it seems more natural ( we have ten fingers and ten toes ). For the computer the binary system is more natural because of its electrical nature ( charged versus uncharged )

Programmers also use the octal ( 8 numbers ) and hexadecimal ( 16 numbers ) number systems because they map nicely in to the binary system. Each octal digit represents exactly 3 binary digits and each hexadecimal digit represents 4 binary digits.

2. Decimal

Decimal refers to numbers in base 10 ( the numbers we use in every day life ). For example the following are decimal numbers.

 

9

100345000

- 256

Note that a decimal number is not necessarily a number with a decimal point in it. Numbers with decimal points ( ie numbers with a fractional part ) are called fixed point or floating point numbers. In addition to the decimal format computer data is often represented in Binary, Octal and Hexadecimal formats.

3. Octal

Octal refers to a base 8 number system, which uses just 8 unique symbols ( 0, 1, 2, 3, 4, 5, 6, 7 ).

Programs often display data in octal format because it is relatively easy for humans to read and can easily be translated in to binary format, which is the most important format for computers.

By contrast decimal format is the easiest format for humans to read, because it is the one we use in every day life but translating between decimal and binary formats is relatively difficult.

In octal format each digits represents three binary digits as shown below.

Octal Number – 3456   Equivalent Binary – 011 100 101 110

4. Hexadecimal

Hexadecimal refers to the base 16 number system, which consists of 16 unique symbols. The numbers 0 to 9 and letter A to F. For example the decimal number 15 is represented as F in the hexadecimal system.

The hexadecimal system is useful because it can represent every byte ( 8 bits ) as two consecutive hexadecimal digits. It is easier for humans to read hexadecimal numbers than binary numbers. Hexadecimal numbers have either an 0x prefix or an h suffix.

To convert a value from hexadecimal to binary, merely translate each hexadecimal digit in to its 4 bit binary equivalent as shown below.

Hexadecimal Number – 0x3F7A   Equivalent Binary – 0011 1111 0111 1010

Binary Conversions

1. Decimal to Binary

Solution – Mathematical conversion of the value by the continuous division by 2.

Example : Decimal Number 25 or  ( 25 )10 to Binary

 

 

 

 

 

 

 

2. Octal to Binary

Solution – In octal format, each digit represents three binary digits. Each digit is mathematically converted in to binary.

Example: Octal Number 3456 or ( 3456)8  to binary

3 4 5 6  = 011  100  101  110

3. Hexadecimal to Binary

Solution – To convert a value from hexadecimal to binary, merely translate each hexadecimal digit in to its four bit binary equivalent by referring Binary Table for Hexadecimal Values. Hexadecimal numbers have either an 0x prefix or an h suffix.

Example: Hexadecimal Number Ox3F7A or (Ox3F7A)16 to binary

Ox3F7A  =  0011    1111   0111   1010

4. Binary to Decimal

Example: 11001  to Decimal

Value is power of 2

= 1 x 2 4 + 1x 2 3 + 0 x 2 2 + 0 X 2 1 + 1 X 2 0

= 16 + 8 + 0 + 0 + 1

= 25

5. Binary to Octal

Example: 011100101110

Binary values in 3 units

Value is power of 2

= 011   100   101  110

=  0 x 22 + 1×21+ 1 x 20   1×22 + 0 x 21 + 0 x 20  : 1×22 + 0×21 + 1×20: 1×22 + 1×21 + 0 x 20

= 0 + 2 + 1 : 4 + 0 + 0 : 4 + 0 + 1 : 4 + 2 + 0

= 3 4 5 6

6. Binary to Hexadecimal

Example: 0011111101111010

Binary values in 4 units

Value is power of 2

= 0x : 0011 : 1111 : 0111 : 1010

= 0 x 23 + 0×22+ 1 x 21 + 1×20  : 1 x 23 + 1×22+ 1 x 21 + 1×20: 0 x 23 + 1×22+ 1 x 21 + 1×20: 1 x 23 + 0×22+ 1 x 21 + 0×20

= 0 + 0 + 2 +1 : 8 + 4 + 2 + 1 : 0 + 4 + 2 + 1 : 8 + 0 + 2 + 0

= 3 : 15 : 7 : 10

= 0x 3 F 7 A

 

Binary Computer Codes

There are different types of Binary Computer Codes ( Binary Coded Decimal )

  4 – bit BCD code ( 24 )

Four bits can be arranged in 24 (16) possible different ways or 16 characters can be represented.

This format uses four bits to represent a character.

 

 6 – bit BCD code ( 26 )

Six bits can be arranged in 26 (64) possible different ways or 64 characters can be represented.

Characters Used

Decimal Digits – 10 Nos.
Capital Alphabetic Letters – 26 Nos.
Other Special Symbols – 28 Nos.

This format uses six bits to represent a character


8 – bit BCD code ( 28 )

Eight bits can be arranged in 28 (256) possible different ways or 256 characters can be represented. There are two commonly used eight bit codes, they are

  1. ASCII – American Standard Code for Information Interchange : Developed by American Standards Institute.
  2. EBCDIC – Extended Binary Coded Decimal Interchange Code : Developed by IBM

Characters Used:

Decimal Digits – 10 Nos.
Capital Alphabetic Letters – 26 Nos.
Other Special Symbols – 28 Nos.
Lowercase Alphabetic Letters – 26 Nos.
Plus All other characters of ASCII or EBCDIC

This format uses eight bits to represent a character

8 – Bit Tables

ASCII Table

 

EBCDIC Table 

 

 

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