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

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

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

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

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

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:

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

Your turn. Convert 1000100112 to decimal
= 275 …. And now, for more about number systems.

Part 2 Number Systems

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

Quick Review: binary to decimal
=77

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

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

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

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

Do this one A10E16  decimal 41230

Octal Base 8 Uses 8 different digits

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

Do this one: 94610  octal 16628

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

Do this one 20458 106110

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

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

Practice Hex  Binary  Hex
Convert E5816 to Binary Convert to Hexadecimal 196

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

Practice Octal  Binary  Octal
Convert 3078 to Binary Convert to Octal 646

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

Practice Octal  Hex Convert 3078 to Hex 11 000 111 first in binary
divide into groups of 4 C716

Practice Hex  Octal Convert 2B1D16 to Octal
first in binary divide into groups of 3 254358

The End