3The 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 useIn base 10 the largest digit is 9The place values are powers of 10:1’s 10010’s 101100’s 1021000’s 103Etc.
5Binary 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 0The place values are powers of 2first 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.
6Binary Sample Place Value Chart 12864321684212726252423222120
7Converting 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
10Converting Base 10 To Base 2 To convert from decimal to binary we break up the decimal number into binary place valuesFind the largest place value you can divide the decimal number intoPut a 1 in that place valueFind 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:
13Hexadecimal 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 10-15A=10 B=11 C=12 D= E=14 F=15The place values are powers of 16The first place value is (1)The second place value is 161 (16)The third place value is 162 (256)The fourth place value is 163 (4096)Etc…
15Hexadecimal Place Value Chart 655364096256161165164163162161160
16Converting 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 chartThen add all these values to get a totalFor example:
19Converting Base 10 to Base 16 To convert a number from decimal to hexadecimal, find the largest place value that can fit into the numberFind out how many times it can go into the number and write that digitIf the digit is larger than 9, convert it to its corresponding letterFind the remainder (by subtracting the previous amount by the new amount) then repeat the above steps until there is no remainderFor example:
22Converting Base 16 To Base 2 To convert from hexadecimal to binary, take each digit in the base 16 number and write out the binary equivalentEach digit must have four binary digits after converting itCombine all the binary numbers you just wrote out
23Base 2 vs. Base 1600000001100102001130100401015011060111710008100191010A1011B1100C1101D1110E1111F
25Converting Base 2 To Base 16 To convert binary to hexadecimal, first break the binary number into groups of four digitsConvert these groups to decimal numbersUse these numbers as the digits for the hexadecimal numberIf the number is greater than 9, change it its corresponding letter (A - F)