1 / 16

Number Systems

This guide covers the essential aspects of number systems: Decimal (base 10), Binary (base 2), Octal (base 8), and Hexadecimal (base 16). Each system has unique symbols and characteristics, providing a foundation for understanding numerical representations in computing. Learn about conversions between systems, the largest symbols in each system, and the significance of weight origins. Whether you're looking to grasp decimal operations or convert between binary and hexadecimal, this resource is a comprehensive starting point.

tobias-hatfield
Download Presentation

Number Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Number Systems

  2. Decimal Numbers Decimal stands for 10 Decimal is the base 10 Number System It has 10 unique symbols 0 1 2 3 4 5 6 7 8 9 The largest symbol is the base – 1 10 – 1 = 9 9 is the largest symbol in Decimal numbers

  3. Decimal Numbers 1000 100 10 units 4 3 5 6 4000 300 50 + 6 435610

  4. Decimal Numbers Weight origin 103 102 101 100 Weights 1000 100 10 1 Number MSD 6 3 6 4 LSD 6000 300 60 + 4 636410

  5. Binary Numbers Binary stands for 2 Binary is the base 2 number system It has two unique symbols 0 and 1 The largest symbol in Binary is the base – 1 2 – 1 = 1 1 is the largest symbol in the Binary Number system

  6. Binary Numbers Weight origin 23 22 21 20 Weights 8 4 2 1 Number 1 0 1 12 8 0 2 + 1 1110

  7. Counting in Binary Weight 8 4 2 1 decimal 0 0 0 0 0 0 0 0 1 1 0 0 1 0 2 0 0 1 1 3 0 1 0 0 4 0 1 0 1 5 0 1 1 0 6 0 1 1 1 7 1 0 0 0 8 1 0 0 1 9 1 0 1 0 10 1 0 1 1 11 1 1 0 0 12 1 1 0 1 13 1 1 1 0 14 1 1 1 1 15

  8. Converting from Decimal to Binary The decimal number 55 = ____ In binary 55 ÷ 2 = 27.5* 1 LSB 27 ÷ 2 = 13.5 1 13 ÷ 2 = 6.5 1 6 ÷ 2 = 3.0 0 3 ÷ 2 = 1.5 1 1 ÷ 2 = 0.5 1 MSB 110111 = 5510 * If the remainder is .5 place a 1 to the right. If 0 place 0 to right

  9. Octal Number System Octal stands for Eight Octal is the base 8 Number System It has 8 unique symbols 0 1 2 3 4 5 6 7 The largest symbol is the base – 1 8 – 1 = 7 7 is the largest symbol in the Octal number system

  10. Octal Number System Weight origin 83 82 81 80 Weights 512 64 8 1 Number 2 1 6 78 1024 64 48 + 7 114310

  11. Hexadecimal Number System Hex = 6 and Decimal = 10 6+10 = 16 Hex is the base 16 Number System It has 16 symbols 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 It must have 16 UNIQUE Symbols 0 1 2 3 4 5 6 7 8 9 A B C D E F The largest symbol is 16 – 1 = 15 or F

  12. Hexadecimal Number System Weight origin 163 162 161 160 Weights 4096 256 16 1 Number 1 2 A F 16 4096 512 160 + 15 478310

  13. Octal Conversions The largest symbol in Octal is 7 It requires three binary bit to represent the number 7  1112 To convert a binary number to Octal, start with the LSB and mark off groups of 3. 101011010010 LSB 101-011-010-010 Write Octal symbol below 5 3 2 28

  14. Octal Conversions To convert an Octal number to binary: Write the three bit binary equivalent below 1 5 6 48 001 101 110 100 = 11011101002 Leading zeros can be left off.

  15. Convert Binary to Hex The largest symbol in Hex is 15 or F It requires four binary bits to represent the number 15 or the symbol F  11112 To convert a binary number to Hex, start with the LSB and mark off groups of 4. 1011001110101110LSB 1011-0011-1010-1110 Write Hex symbols below B 3 A E 16

  16. Convert Hex to Binary To convert Hex to Binary, write the 4 bit Binary equivalent below each Hex digit. A 6 3 F 16 1010 0110 0011 1111 = 10100110001111112

More Related