# Why Hexadecimal, Octal and Binary?

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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#### Solution Preview

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.

Boolean Algebra and circuit design

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