Common Number Systems, Slides of Computer science

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Unit

Number Systems

College of Computer and Information Sciences Department of Computer Science CSC 220: Computer Organization

Quantities/Counting (1 of 3)

Decimal Binary Octal

Hexa- decimal 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7

Quantities/Counting (2 of 3)

Decimal Binary Octal

Hexa- decimal 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F

Conversion Among Bases

• The possibilities:

Hexadecimal

Decimal Octal

Binary

Decimal to Decimal (just for fun)

Hexadecimal

Decimal Octal

Binary

12510 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125

Base

Weight

Binary to Decimal

• Technique
  • Multiply each bit by 2n^ , where n is the “weight”

of the bit

• The weight is the position of the bit, starting

from 0 on the right

• Add the results

Example

• 1010112 => 1 x 2 0 =
  • 1 x 2 1 =
  • 0 x 2 2 =
  • 1 x 2 3 =
  • 0 x 2 4 =
  • 1 x 2 5 =
    • 43

Octal to Decimal

Hexadecimal

Decimal Octal

Binary

Octal to Decimal

• Technique
  • Multiply each bit by 8n^ , where n is the “weight”

of the bit

• The weight is the position of the bit, starting

from 0 on the right

• Add the results

Hexadecimal to Decimal

Hexadecimal

Decimal Octal

Binary

Hexadecimal to Decimal

• Technique
  • Multiply each bit by 16n^ , where n is the

“weight” of the bit

• The weight is the position of the bit, starting

from 0 on the right

• Add the results