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Why Hexadecimal, Octal and Binary?

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Why would anyone use hexadecimal or Octal nowadays? Also why binary?

What types of data formats are there? Why are there so many? Can you tell from looking at a string of bits exactly what the data represents?

Can you please point me in the direction of references that would shed some light?

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Why would anyone use hexadecimal or Octal nowadays? Also why binary?
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Why binary?
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The basic unit of storage in a computer is the bit (binary digit). The bit can have one of two values: 0 or 1. This is easier to implement in hardware than a unit that can take on 10 different values as people use in every day activities.
Bit could be represented by a transistor being off (corresponds to value 0) or on (corresponds to value 1).
Binary also has a convenient and natural association with logical values of False (0) and True (1).

They group binary bits altogether to allow them to represent more information. For instance:
- A group of 4 bits is known as nybble is , e.g. 1101
- A group of 8 bits is a byte, e.g. 11010011
- A group of 32 bits is known as a word.

Computers have been designed with various word sizes of: 36, 48, or 60 bits.

The number of possible combinations of a group of N bits is 2^N = 2x2x2 ... x2 (N 2s). Therefore:
- A nybble can form 2^4=16 combinations
- A byte can form 2^8=256 combinations
- A 32-bit word can form 2^32=4,294,967,296 combinations

It is also possible to represent symbols and numbers using binary - combinations of a group of bits.
* For instance, bytes can be used to represent text by associating each byte value with a character. The ISO-8859-1 character encoding (an extension of the ASCII code) assigns the value 00101110 to mean a period ('.'), 01000001 to mean capital 'A', and so on.
* The binary numbering system is like the decimal system, except that the only two digits used are 0 and 1, and digits are multiplied by powers of 2 instead of 10. For instance, in ...

Solution Summary

Hexadecimal, Octal and Binary system nowadays are explored. Types of data formats are decribed.

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2. Convert the following decimal numbers to their binary, octal, and hexadecimal equivalents

a. 16
b. 32
c. 48
d. 80

3. Do the following work and answer the following questions:

a. Explain the relationship between an AND gate and a NAND gate in terms of Boolean Algebra and draw truth tables for both types of gate
b. Explain the relationship between an OR gate and a NOR gate in terms of Boolean Algebra and draw truth tables for both types of gate

4. In the following problems, use 0 to stand for False and 1 to stand for True. Indicate whether the answer is true or false

a. Jack is a boy AND Jill is a girl
b. Jack is NOT a girl
c. Jack is a boy OR Jill is a boy
d. Jack is NOT a boy AND Jill is NOT a boy
e. Jack is a boy OR Jill is NOT a boy

5. Fill in the following truth tables

A B NOT A NOT B A OR B NOT (A OR B) A AND B NOT A AND NOT B NOT (A AND B) NOT A OR NOT B
0 0
0 1
1 0
1 1

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