Digital Number System - Computer Logical Organization

What is Digital Number System?

The number system that has few symbols is usually recognized by the Digital system. These symbols are known s digits which depict different values in accordance with their position on the number line.

On the number line the following are used for determining the value of each digit:

  • The digit
  • The position of the digit in the number
  • The base of the number system (base implies the total number of digits in the number system)

What is Decimal Number System?

The digits from 0 to 9 are used by the decimal number system and thus carry a base 10. To the left of the decimal point, the successive positions are units, tens, hundreds, thousand etc.

An explicit power of base (10) is represented by each position. For instance, the decimal number 6578 has 8 in units place, 7 in tens place, 5 in hundreds place and 6 in thousands place. The value of the decimal number is represented as:

Some of the number systems which are widely used in computer systems are tabulateb below:

S.N.
Number System & Description
1
Binary Number System
Base 2. Digits used: 0, 1
2
Octal Number System
Base 8. Digits used: 0 to 7
3
Hexa Decimal Number System
Base 16. Digits used: 0 to 9, Letters used: A- F

What is Binary Number System?

The following are some of the characteristics of Binary Number System:

  • Only two digits, 0 and 1 are used.
  • The number system is also known as base 2 number system.
  • A 0 power to the base (2) is represented for each of the position.
  • An x power to the base (2) is represented foe the last position of the binary system.

Example

Binary Number:

Calculating Decimal Equivalent

Step
Binary Number
Decimal Number
Step 1
101012
((1 × 24) + (0 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10
Step 2
101012
(16 + 0 + 4 + 0 + 1)10
Step 3
101012
2110

What is Octal Number System?

The following are some of the characteristics of Octal Number System:

  • Eight digits 0,1,2,3,4,5,6,7 are used.
  • Octal Number System is also known as base 8 number system.
  • A 0 power to the base (8) is represented for each of the position.
  • An x power to the base (8) is represented foe the last position of the Octal Number system.

Example

Octal Number −

Calculating Decimal Equivalent

Step
Octal Number
Decimal Number
Step 1
125708
((1 × 84) + (2 × 83) + (5 × 82) + (7 × 81) + (0 × 80))10
Step 2
125708
(4096 + 1024 + 320 + 56 + 0)10
Step 3
125708
549610

What is Hexadecimal Number System?

The following are some of the characteristics of Octal Number System:

  • Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
  • Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
  • Hexadecimal Number System is also known as base 16 number system.
  • A 0 power to the base (16) is represented for each of the position.
  • An x power to the base (16) is represented foe the last position of the Hexadecimal Number system

Example −

Hexadecimal Number:

Calculating Decimal Equivalent

Step
Hexadecimal Number
Decimal Number
Step 1
19FDE16
((1 × 164) + (9 × 163) + (F × 162) + (D × 161) + (E × 160))10
Step 2
19FDE16
((1 × 164) + (9 × 163) + (15 × 162) + (13 × 161) + (14 × 160))10
Step 3
19FDE16
(65536 + 36864 + 3840 + 208 + 14)10
Step 4
19FDE16
10646210

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