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Published byJacquelyn Earnest Modified about 1 year ago

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Number Systems Different number systems Representation of numbers in binary Conversion between decimal and binary, Conversion between binary and hexadecimal Use of subscripts 2, 10 and 16 for bases

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Number Systems Decimal number system – Base 10 = 1, 2,3 4, 5, ect.. Binary number system –Base 2 = 0001, 0010, 0011, ect… Hexadecimal number system = Base 16 = 9, A, B, 4C ect…

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Decimal Number Systems HundredsTensUnits = 341 Decimal numbers are base 10 They are made up of 10 numbers – 0,1,2,3,4,5,6,7,8,9. Combining the ten numbers will create units, tens, hundreds and thousands

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Split the following decimal numbers HundredsTensUnits 550 HundredsTensUnits 982

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Answers HundredsTensUnits = HundredsTensUnits =

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Binary Number System Binary numbers are base 2 Computer language They are made up of 2 numbers – 1 and 0 DecimalBinaryDecimalBinary

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Hexadecimal Number Systems Hexadecimal numbers are base 16 Computer memory locations They are made up of 16 numbers DecimalHexDecimalHex DecimalHex10 A B C D E 16 DecimalHex F 16

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Importance of Base numbers Writing the base numbers is very important as; ◦ and are not the same number but without the base they would be both considered as the same number ◦ and 10 2 are not the same number as 10 2 represents 2 10

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Complete the table NumberNumber System A

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Answers NumberNumber System Decimal 2A 16 Hexadecimal Binary Decimal Hexadecimal Binary

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Converting Binary to Decimal

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Explanation 1. Write down the placement value on top of each number. 2. Write the values that are on (the ones with a one under them 3. Add the numbers together

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Example We want to convert to decimal

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Working Convert the following to decimal

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Answers Convert the following to decimal = = = = =

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Converting Decimal to Binary

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Method One 1. Write down the placement values of binary 2. Chose the numbers that add up to you decimal number 3. Put a 1 under the numbers used to add up to your decimal number

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Example Convert to binary = =

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Method Two Divide the original number by 2 and write down the remainder even if it is 0 Keep on dividing the decimal numbers by 2 until 1 is divided by 2 Write down the remainders next to each other starting from the bottom moving upwards

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Example Convert to binary Ans = /2=23r0 /2=11r1 /2=5r1 5/2=2r1 2/2=1r0 1/2=0r1

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Working Convert the following decimal numbers to binary

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Answers Convert the following decimal numbers to binary = = = = =

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Converting Binary to Hexadecimal

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Explanation Split the binary number into groups of = 0100 – 1110 Write the 2 x on top of each number starting from the right Add the numbers that are on Write down the totals, if a total is larger than 9, convert it to the hex letter E 16 NOTE: when we do not have enough bits lefts to create a group of 4 we add 0s

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Example Convert in Hexadecinal

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Working Convert the following into Hexadecimal

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Working Convert the following into Hexadecimal = 1D = = 2A = = 71 16

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Converting Hexadecimal to Binary

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Explanation 1. Write each individual number in the hexadecimal number eg B Write the binary placement values for each hex number 3. List 1s under the placement values that are on B = Write the split binary number as one whole number

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Example Convert 2C 16 to binary 2C =

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Working Convert the following hex numbers to binary 1. AB F CC

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Answers Convert the following hex numbers to binary 1. AB 16 = F7 16 = = CC 16 = =

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Converting Decimal to Hexadecimal

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Method One Divide the decimal number by 16 taking note of the remainders Keep on dividing the whole number by 16 until the whole number obtained is 0. Write down the remainders next to each other starting from the bottom, changing numbers greater than 9 to letters 465/16=29r1 /16=1r13 1/16=0r1 ANS = 1D1 16

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Example Convert to hexadecimal 800/16=50r0 /16=3r2 3/ =0r3 ANS =

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Method Two 1. Convert the decimal number to binary 2. Convert the binary number to hexadecimal Eg, changing to hexadecimal

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Example Convert to hexadecimal = =

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Working Convert the following to Hexadecimal numbers

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Answers Convert the following to Hexadecimal numbers = = = = = 6F 16

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Converting Hexadecimal to Decimal

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Explanation Writing down the placement values on top of each number starting with 16 0 Multiply the top value with the hexadecimal number. Add all the results A (256x4)(16x3)(1x10) = = Converting 43A 16 to decimal

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Working Convert the following into decimal CB F B

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Answers Convert the following into decimal = B0 16 = F8 16 = B4 16 = =

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Homework Copy and complete this table DecimalBinaryHexadecimal E C

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