 # BINARY 1. Number Systems Base 10 uses the numbers 0-9 Represents numbers as ones, tens, hundreds etc HundredsTensOnesSolution 0430+40+3= 43 594500+90+4=

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BINARY 1

Number Systems Base 10 uses the numbers 0-9 Represents numbers as ones, tens, hundreds etc HundredsTensOnesSolution 0430+40+3= 43 594500+90+4= 594

Number Systems Base 2 uses the numbers 0-1 Each column is a factor of two To calculate a conversion we add together the things that are included (1) and not the things that aren’t (0) 1286464 3232 1616 8421Solution 00010001 01010010 10000100 11001001 128 6432168421 Solution 0001000116 + 1 = 17 0101001064 + 16 + 2 = 82 10000100128 + 4 = 132 11001001128 + 64 + 8 + 1 = 201

Binary to Decimal Conversion Practise converting the following binary to decimal 1286432168421Solution 00101100 01011000 10100011 11000011 11111000 01110001 01010101 01100110 11111111

Binary to Decimal Conversion SOLUTIONS 1286432168421Solution 0010110032 + 8 + 4 = 44 0101100064 + 16 + 8 = 88 10100011128 + 32 + 2 + 1 = 163 11000011128 + 64 +2 + 1 = 195 11111000128 + 64 + 32 + 16 + 8 = 248 0111000164 + 32 + 16 + 1 = 113 0101010164 + 16 + 4 + 1 = 85 0110011064 + 32 + 4 + 2 = 102 11111111128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

Decimal to Binary Conversion To convert the other way, we work from the highest number to the lowest number asking if it fits in our decimal number Convert 39 Does 128 fit into 39? No 0 Does 64 fit into 39? No 0 Does 32 fit into 39? Yes 1 how many are left over? 39-32 = 7 Does 16 fit into 7? No 0 Does 8 fit into 7? No 0 Does 4 fit into 7? Yes 1 how many are left over? 7-4 = 3 Does 2 fit into 3? Yes 1 how many are left over? 3-2 = 1 Does 1 fit into 1? Yes 1 how many are left over? 1-1=0 39 is 00100111

Decimal to Binary Conversion Using the method in the previous slide, convert the following decimal solutions to binary 1286432168421Solution 5 19 27 35 49 87 167 232 240

Decimal to Binary Conversion SOLUTIONS 1286432168421Solution 000001015 0001001119 0001101127 0010001135 0011000149 0101011187 10100111167 11101000232 11110000240

Fractional Numbers If a decimal number has values after the decimal point we can still convert using the same process 21..5.5.2 5.125.0625.0312 5.01562 5 Solution 01.100000 10.011000 00.011100 11.100101 21..5.25.125.0625.03125.015625Solution 01.1000001 + 0.5 = 1.5 10.0110002 + 0.25 + 0.125 = 2.375 00.0111000.25 + 0.125 + 0.0625 = 0.4375 11.1001012 + 1 + 0.5 + 0.0625 + 0.015625 = 3.578125

Fractional Numbers Sometimes we find numbers that we can’t easily fit into the binary grid – for these we use another system Division by 2 We repeatedly divide a number by two to get the final solution

Fractional Numbers – Division by 2 Convert 0.4 Multiply it by 2 Put the whole number in one column Put the remainder in the next column Carry your remainder to be the starting number in the next row Repeat these steps There is no rule how many times you should do this... But I accept 5 times NumberMultiplic -ation Whole Number Part number 0.4x 2 =0.8 0.8x 2 = The binary number in the ‘whole number’ column, from top to bottom, is your binary solution

Fractional Numbers – Division by 2 Convert 0.3 NumberMultipli c-ation Whole Number Part number 0.3x 2 = Convert 0.24 NumberMultipli c-ation Whole Number Part number 0.24x 2 =

Characters using Binary When we use 8 bit binary, each combination can be converted into decimal. Each decimal value has a character associated with it. For example:A is 65 a is 97 Your ASCII character set has been provided as a separate handout.

Characters using Binary Convert the following: CharacterDecimal # 100 F 84 p 32

Characters using Binary Solutions CharacterDecimal #35 d100 F70 T84 p112 (space)32

Worksheet Test your new binary decimal conversion skills with worksheet : Binary_1

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