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Binary, Hexadecimal, and Base 10

Binary, Hexadecimal, and Base 10. 8235455. 656. DECIMAL SYSTEM. OR Base 10. 3547553. 12875. The decimal system is also referred to as base 10 A 10 in subscript is put beside any decimal number to show it is in base 10 (ex. 193 10 ) Base 10 is the number system we normally use

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Binary, Hexadecimal, and Base 10

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  1. Binary, Hexadecimal, and Base 10

  2. 8235455 656 DECIMAL SYSTEM OR Base 10 3547553 12875

  3. The decimal system is also referred to as base 10 • A 10 in subscript is put beside any decimal number to show it is in base 10 (ex. 19310) • Base 10 is the number system we normally use • In base 10 the largest digit is 9 • The place values are powers of 10: • 1’s  100 • 10’s  101 • 100’s  102 • 1000’s  103 • Etc.

  4. 0 0 0 0 1 1 0 1 1 0 0 1 1 BINARY 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1

  5. Binary is also referred to as base 2 • A 2 in subscript is put beside any decimal number to show it is base 2 (ex. 1000112) • In base 2, the only digits used are 1 and 0 • The place values are powers of 2 • first place value is 20 (1) • second place value is 21 (2) • third place value is 22 (4) • fourth place value is 23 (8) • fifth place value is 24 (16) • Etc.

  6. Binary Sample Place Value Chart 27 26 25 24 23 22 21 20

  7. Converting Base 2 To Base 10 To convert base 2 (binary) to base 10 (decimal), • Place the binary number from right to left in the place value chart. • If the digit is a 1, then add the value of that place from the place value chart. • If the digit is 0, add 0

  8. 1 0 0 1 0 2 0 = 2 = 0 = 0 = + 16 = 18 10

  9. 1 0 1 1 1 0 0 2 0 = 0 = 4 = 8 = 16 = 0 = + 64 = 92 10

  10. Converting Base 10 To Base 2 • To convert from decimal to binary we break up the decimal number into binary place values • Find the largest place value you can divide the decimal number into • Put a 1 in that place value • Find out how much is left over, then see the next largest place value you can divide the leftover into (any number that can not divide into the number, put a zero) • For example:

  11. 1 1 0 1 13 = Remainders 5 1 1 0 1 1 1 1 0 0 0 114 = 50 18 2 2 2 0 0 1 1 0 1 0 0 1 0 0 420 = 36 4 0 164 36 4 4 0 0 1 1 0 1 0 0 1 1 1 1 0 1694 = 670 158 158 30 30 30 14 6 2 0 0

  12. 27A29B 83B38A298E 2784B47A HEXADECIMAL F83B9464 34B123E3 635F048B

  13. Hexadecimal is also referred to as base 16 • A 16 in subscript is put beside any hexadecimal number to show it is base 16 (ex. 836F89E16) • In base 16, the digits 0-9 are used, as well as the letters A-F to represent the numbers 10-15 A=10 B=11 C=12 D=13 E=14 F=15 • The place values are powers of 16 • The first place value is 160  (1) • The second place value is 161  (16) • The third place value is 162 (256) • The fourth place value is 163 (4096) • Etc…

  14. Base 10 vs. Base 16

  15. Hexadecimal Place Value Chart 165 164 163 162 161 160

  16. Converting Base 16 to Base 10 • To convert a number from hexadecimal to decimal, find the value of each digit in the number, then multiply it by the value in the place value chart • Then add all these values to get a total • For example:

  17. 8 3 2 D 16 2 13 = 32 1 = 768 = 1 32768 + = 3 3 5 8 1 10

  18. 2 A 0 F 16 15 = 0 = 2560 = 8192 + = 1 0 7 6 7 10

  19. Converting Base 10 to Base 16 • To convert a number from decimal to hexadecimal, find the largest place value that can fit into the number • Find out how many times it can go into the number and write that digit • If the digit is larger than 9, convert it to its corresponding letter • Find the remainder (by subtracting the previous amount by the new amount) then repeat the above steps until there is no remainder • For example:

  20. 3 3 5 8 1 3 2 D 8 = 10 13 32768 768 32 Remainder 813 45 13 0

  21. 2 4 8 3 1 0 F F 6 = 10 0 15 24576 240 Remainder 255 255 15 0

  22. Converting Base 16 To Base 2 • To convert from hexadecimal to binary, take each digit in the base 16 number and write out the binary equivalent • Each digit must have four binary digits after converting it • Combine all the binary numbers you just wrote out

  23. Base 2 vs. Base 16

  24. 318 = 16 3 0011 1 0001 8 1000 0011 11 0001 1000 2

  25. Converting Base 2 To Base 16 • To convert binary to hexadecimal, first break the binary number into groups of four digits • Convert these groups to decimal numbers • Use these numbers as the digits for the hexadecimal number • If the number is greater than 9, change it its corresponding letter (A - F)

  26. 0011 1101 1000 2 3 13 8 D 3 D 8 16

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