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Published byBarnard Davidson Modified over 7 years ago

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Number systems Converting numbers between binary, octal, decimal, hexadecimal (the easy way)

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**Small numbers are easy to convert**

But it helps to have a system for converting larger numbers to avoid errors. 1210 = C16 510 -> 1012 11002 = 1210

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**Converting from base 10 (decimal) to base 2 (binary)**

DEMONSTRATE Converting from base 10 (decimal) to base 2 (binary) example number = 42 Write the powers of 2 in a row starting on the RIGHT side with a 1 Keep doubling (*2) until you get to something greater than your number (42) 64 32 16 8 4 2 1 This is too big 1 1 1 3. Write a 1 underneath if that place value is used, 0 if not. subtract to find out what is left. 42 -32 ---- 10 10 - 8 ---- 2 2 -2 ---- Watch Read your answer from left to right The number in binary is

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**Converting from base 10 (decimal) to base 2 (binary)**

DO TOGETHER Converting from base 10 (decimal) to base 2 (binary) example number = 7053 write the powers of 2 in a row until you get to something > the number 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1 Too big 1 1 1 1 1 1 1 1 7053 -4096 2957 2957 -2048 909 909 - 512 397 397 -256 ------ 141 141 -128 13 13 - 8 ----- 5 5 -4 --- 1 1 -1 --- Do this together the number in binary is

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STUDENT’S TURN Do this one binary 1 2 4 8 16 32 64 128 256 1 Too big 1 1 1 Click to see each digit that is needed. The answer is:

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**To convert binary to decimal**

the number in binary is Write the powers of 2 below each digit and only add the values with a 1 above them. Start at the right and double each number = 1,485 Watch

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**Your turn. Convert 1000100112 to decimal**

= 275 …. And now, for more about number systems.

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Part 2 Number Systems

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**Quick review What’s 41 in binary? 32 16 8 4 2 1 1 0 1 0 0 1**

The answer is:

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**Quick Review: binary to decimal**

=77

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**An Introduction to Hexadecimal**

16 digits Use letters when you run out of single digits A B C D E F SO… = ?16 B16 1510 = ? F16 1610 = ? 1016

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**from base 10 to base 16 (decimal to hexadecimal)**

example number = 7053 write the powers of 16 in a row until you get to one > the number divide the number by each power of 16 and write the answer and save the remainder 65,536 4, Too high 7053/ = R 2957 2957/256 = R 141 141/16 = 8 R 13 13 ones the numbers in hex are: A B C D E F (A=10…. F=15) So your number is = 1B8D16 Watch

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Do this one 96210 hexadecimal 3C216 This is 3*256 + C(10)*16 + 2

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**from hexadecimal (base 16) back to decimal**

Watch 1B8D16 Write the number across a row. Write the powers of 16 below it. Multiply. Then add the products. B D =(1X4096)+ (11*256)+ (8*16)+(13*1) = = 7053 4096 256 16 1

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Do this one A10E16 decimal 41230

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Octal Base 8 Uses 8 different digits

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**from base 10 to base 8 (decimal to octal)**

example number = 7053 write the powers of 8 in a row until you get to one > the number divide the number by each power of 8 write the answer and save the remainder too high 7053/ = R 2957 2957/ = 5 R 397 397/64 = 6 R 13 13/8 = 1 R 5 = 5 ones so your number in octal is Watch

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Do this one: 94610 octal 16628

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**from octal (base 8) back to decimal**

156158 write the number write the powers of 8 below it and multiply. then add the products. 1 * = 4096 5 * 512 = 2560 6 * 64 = 384 1* 8 = 5 * 1 = added together = 7053 Watch

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Do this one 20458 106110

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1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 Binary hex octal If you can count from 1 to 15 in binary you have it made

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**Binary to hexadecimal and hex to binary**

Watch 4 binary digits correspond to 1 hexadecimal digit Start grouping digits on the RIGHT side 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F To convert binary to hex Binary Hexadecimal E 35E16 Write this down the side of your paper. Hex Binary 28D1

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**Practice Hex Binary Hex**

Convert E5816 to Binary Convert to Hexadecimal 196

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**binary to octal and octal to binary**

3 binary digits correspond to 1 octal digit 000 0 001 1 010 2 011 3 100 4 101 5 110 6 111 7 Binary to octal 263 Octal to binary 451 101001 Watch

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**Practice Octal Binary Octal**

Convert 3078 to Binary Convert to Octal 646

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**octal to hex and hex to octal.**

Convert to binary, regroup and convert to other base. Octal to binary to hex 4518 12916 Watch

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**Practice Octal Hex Convert 3078 to Hex 11 000 111 first in binary**

divide into groups of 4 C716

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**Practice Hex Octal Convert 2B1D16 to Octal**

first in binary divide into groups of 3 254358

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The End

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