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Name_______________________________________Date______________________Intro to Computer ScienceMr. SurielBase Conversion Review Sheet4 Important Number BasesName of BasesDefinitionExamplesBase 10 or DecimalNORMAL NUMBERSNumbers composed of the symbols 0 to 9.281, 92, 3,…Base 2 or BinaryA digit of a binary number is called a bit.Numbers composed of the symbols 0 and 1.1011, 110, 1, 0, 1100011,…10011 is a 5 bit number. Base 8 or OctalNumbers composed of the symbols 0 to 7.72, 1, 70, 31,…Base 16 or HexadecimalNumbers composed of the symbols 0 to 9 and A, B, C, D, E.Note:A = 10B = 11C = 12D = 13E = 14F = 15281, A34, CAF, FE98,…You need to know how to convert between the bases.Converting from base 2 to base 10The right most bit represents the number 1 Going from RIGHT to LEFT, each bit is double the previous bit.Add the bits that have the value 1Ignore the bits with a 0Example: Convert 10011012 to base 10.left16673300Step 1) Figure out what each bit is worthStep 2) Add the bits that have a value of 164 + 8 + 4 + 1 = 77Therefore, the answer is 7710Practice:Convert the binary numbers to decimal.1) 1001122) 11012Converting from base 10 to base 2Apply the concept from above. Find the LARGEST power of 2 that can go into the given base 10 number. Make that bit 1, then go backwards and fill in the bits that add to the given number.Example:Convert 5910 to binary.1428757366000491490110795100Step 1) Find the largest power of 2 that goes into 59.Step 2) Fill in the numbers the blanks32 is the largest, therefore the binary number will look like 1 if it helps it add to 59 and 0 if it doesn’tTherefore, the answer is 1110112Practice:try in your notebookConvert the decimal numbers to binary.3) 68104) 2910----------------------------------------------------------------------------------------------------------------------------------------------------------------Relationship from base 2 of base 8All you need to know is, every 3 bits of a binary number equals one digit of a base 8 number. (Starting from the right)Example:Convert 10011 to octal46958256096000left8133500Step 1) Group the bits in groups of 3, starting from the right. Step 2) Convert each group, each group is a digit. 2 3Therefore, the answer is 238Practice:try in your notebookConvert the binary number to octal.Convert the octal number to binary5) 1010111126) 478----------------------------------------------------------------------------------------------------------------------------------------------------------------Relationship from base 2 of base 16All you need to know is, every 4 bits of a binary number equals one digit of a base 16 number. (Starting from the right)Example:Convert 11011011 to hexadecimal4695825889000left889000Step 2) Convert each group, each group is aStep 1) Group the bits in groups of 4, starting from the right. digit. 1311Recall from the chart D = 13 and B = 11Therefore, the answer is DB16 Practice:try in your notebookConvert the binary number to hexadecimal.Convert the base 16 number to base 2.7) 1010111128) C916 ................
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