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Published byCassandra Ribbens Modified over 2 years ago

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OR Base 10

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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 ) 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 10 0 –10’s 10 1 –100’s 10 2 –1000’s 10 3 –Etc.

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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 ) In base 2, the only digits used are 1 and 0 The place values are powers of 2 –first place value is 2 0 (1) –second place value is 2 1 (2) –third place value is 2 2 (4) –fourth place value is 2 3 (8) –fifth place value is 2 4 (16) –Etc.

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Binary Sample Place Value Chart

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Converting Base 2 To Base 10 To convert base 2 (binary) to base 10 (decimal), 1.Place the binary number from right to left in the place value chart. 2.If the digit is a 1, then add the value of that place from the place value chart. 3.If the digit is 0, add 0

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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: Converting Base 10 To Base 2

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Remainders

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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. 836F89E 16 ) In base 16, the digits 0-9 are used, as well as the letters A-F to represent the numbers A=10 B=11 C=12 D=13 E=14 F=15 The place values are powers of 16 –The first place value is 16 0 (1) –The second place value is 16 1 (16) –The third place value is 16 2 (256) –The fourth place value is 16 3 (4096) –Etc…

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Base 10 vs. Base A 11B 12C 13D 14E 15F

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Hexadecimal Place Value Chart

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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:

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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:

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Remainder

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Remainder

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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

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Base 2 vs. Base A 1011B 1100C 1101D 1110E 1111F

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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)

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