1 / 15

Number Systems

Number Systems. Benchmark Companies Inc PO Box 473768 Aurora CO 80047. Number Systems:. Decimal Binary Hexadecimal Octal Binary Coded Decimal (BCD). 10 digits: 0 1 2 3 4 5 6 7 8 9 Counting beyond 9 requires additional place values to begin. This will go on to infinity: i.e.

talli
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 Benchmark Companies Inc PO Box 473768 Aurora CO 80047

  2. Number Systems: • Decimal • Binary • Hexadecimal • Octal • Binary Coded Decimal (BCD)

  3. 10 digits: 0 1 2 3 4 5 6 7 8 9 Counting beyond 9 requires additional place values to begin. This will go on to infinity: i.e. … 8,9,10,11……98,99,100,101…999,1000,... The Decimal System The decimal system is a base 10 (modulo 10) number system:

  4. Counting beyond 9 requires additional place values as powers of 10: ______ ______ ______ ______ ______ . _____ 10000 1000 100 10 1 .1 (104) (103) (102) (101) (100) . (10-1) 1 w/4 0’s 1 w/3 0’s 1 w/2 0’s 1 w/1 0’s 1 w/0 0’s . The Decimal System

  5. The Binary System: 2 digits: 0 or 1 (in digital terms, logic 0 or logic 1) Counting beyond 1 requires additional place values. This will go on to infinity: i.e. 0,1,10,11,100,101,110,111,1000,1001,... The Binary System is a base 2 (mod 2) number system:

  6. The Binary System: 2 digits: 0 or 1 (in digital terms, logic 0 or logic 1) Counting beyond 1 requires additional place values as powers of 2: ______ ______ ______ ______ ______ . _____ 16 8 4 2 1 .5 (24) (23) (22) (21) (20) . (2-1) The Binary System is a base 2 (mod 2) number system:

  7. Example:Convert 3710 to binary. It is important to be able to convert binary to decimal and vice-versa. In this example, convert 37 base 10 to it’s binary (base 2) equivalent number. Base 10 >>> Base 2

  8. Example:Convert 3710 to binary. METHOD I: Sum-of-weights: ____ ____ ____ ____ ____ ____ 32 16 8 4 2 1 METHOD II: Repeated-division-by-base (here, base 2) • 37/2 = 18 remainder of 1 This is your LSB • 18/2 = 9 remainder of 0 • 9/2 = 4 remainder of 1 • 4/2 = 2 remainder of 0 • 2/2 = 1 remainder of 0 • ½ = 0 remainder of 1 This is your MSB This process gives you the same result: 3710 is 100101 in binary. 1 0 0 1 0 1

  9. Example:Convert 10110102 to decimal: In this example, convert 1011010 base 2 to it’s decimal (base 10) equivalent number. Base 2 >>> Base 10

  10. Example:Convert 10110102 to decimal: Sum-of-weights uses total of each place value: 1x26 + 0x25 + 1x24 + 1x23 + 0x22 + 1x21 +0x20 1x64 + 0x32 + 1x16 + 1x8 + 0x4 + 1x2 + 0x 1 64 + 0 + 16 + 8 + 0 + 2 + 0 = 9010

  11. The Hexadecimal System “Hexa” = 6 “Decimal” = 10 16 digits: 0123456789 A b C d E F representing decimal 10 through decimal 15 (use of lower case helps differentiate between b and 8 or d and 0 in a digital display) The Hexadecimal system is a base 16 (mod 16) number system:

  12. Convert 5810 to hexadecimal: Sum-of-weights: ____ ____ ____ 256 16 1 Check: 3x16 + 10x1 = 48+10 = 5810 = 3A16 ***Repeated division-by-base is most effective for larger conversions. 0 3 A

  13. Tips for Conversions: THE SHORTCUT FOR CONVERTING BINARY TO HEXADECIMAL HEXADECIMAL TO BINARY Since there is a relationship between 2 and 16 (24 = 16), there is a relationship between the place values in binary and the place values in hexadecimal – look for groups of 4 instead of 3. Example: Convert 101101012 to hexadecimal: 1011 0101 = b516

  14. Tips for Conversions (Continued): Convert 3F716 to binary: *Remember to represent each digit as a 4-bit binary word!* 0011 1111 0111 Drop initial 0’s to simplify. 3F716 = 1111110111

  15. Binary Coded Decimals (BCD) • Uses a 4-bit binary representation of each digit in decimal • Example: 672 in BCD would be 0110 0111 0010 • Example: 1001 0110 0101 1000 is BCD for 9658 • ***In BCD, there will not be values beyond 1001 (decimal 9)

More Related