Number systems Converting numbers between binary, octal, decimal, hexadecimal (the easy way)
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Transcript of 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)
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Small numbers are easy to convert
But it helps to have a system for converting larger numbers to avoid errors.
5 10 ->
101 2
1210 = C16
11002 = 12
10
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Converting from base 10 (decimal)to base 2 (binary) example number = 42
3. Write a 1 underneath if that place value is used, 0 if not. subtract to find out what is left.
Read your answer from left to rightThe number in binary is 101010
1. Write the powers of 2 in a row starting on the RIGHT side with a 1 2. Keep doubling (*2) until you get to something greater than your number (42)
DEMONSTRATE
Watch
12481632641 0 1 0 1 0
42
-32
----
10
10
- 8
----
2
2
-2
----
0
This is too big
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Converting from base 10 (decimal)to base 2 (binary) example number = 7053
the number in binary is 1101110001101
write the powers of 2 in a row until you get to something > the number
DO TOGETHER
Do this together
12481632641282565121024204840968192
1
7053
-4096
-------
2957
1
2957
-2048
-------
909
0 1
909
- 512
-------
397
1
397
-256
------
141
1
141
-128
-------
13
0 0 0 1
13
- 8
-----
5
1
5
-4
---
1
1
1
-1
---
0
0Too
big
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Do this one 15010 binary
124816
32
64
128
256
The answer is: 10010110
STUDENT’S TURN
1 0 0 1 0 1 1 0Click to see each digit that is needed.
Too big
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To convert binary to decimal Write the powers of 2 below each digit and only add the values with a 1 above them.
the number in binary is 10111001101
1 0 1 1 1 0 0 1 1 0 1
1024 512 256 128 64 32 16 8 4 2 1
Watch
1024 + 256+128+64 + 8 + 4 + 1 = 1,485
Start at the right and double each number
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Your turn. Convert 1000100112 to decimal 1 0 0 0 1 0 0 1 1 256 128 64 32 16 8 4 2 1
256 + 16 + 2+1 = 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?
The answer is: 101001
64 32 16 8 4 2 1
1 0 1 0 0 1
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Quick Review: binary to decimal
10011012 decimal 64 + 8 + 4 + 1 =77
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An Introduction toHexadecimal 16 digits Use letters when you run out of single digits 0 1 2 3 4 5 6 7 8 9 A B C D E F SO… 1110 = ?16
B16
1510 = ? F16
1610 = ? 1016
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from base 10 to base 16 (decimal to hexadecimal) 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 4,096 256 16 1 Too high 7053/4096 = 1 R 2957 2957/256 = 11 R 141 141/16 = 8 R 13 13 ones
the numbers in hex are: 1 2 3 4 5 6 7 8 9 A B C D E F (A=10…. F=15)
So your number is 1 11 8 13 = 1B8D16
example number = 7053
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 Write the number across a row. Write the powers of 16
below it. Multiply. Then add the products. 1 B 8 D
=(1X4096)+ (11*256)+ (8*16)+(13*1) = 4096 + 2816 + 128 + 13 = 7053
1B8D16
1162564096
Watch
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Do this one
A10E16 decimal
41230
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Octal
Base 8
Uses 8 different digits
0 1 2 3 4 5 6 7
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from base 10 to base 8(decimal to octal) 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 32768 4096 512 64 8 1 too high
7053/4096 = 1 R 2957 2957/512 = 5 R 397 397/64 = 6 R 13 13/8 = 1 R 5 = 5 ones
so your number in octal is 156158
example number = 7053
Watch
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Do this one:
94610 octal
16628
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from octal (base 8) back to decimal
write the number write the powers of 8 below it and multiply. then add the
products. 1 5 6 1 5 4096 512 64 8 1 1 *4096 = 4096 5 * 512 = 2560 6 * 64 = 384 1* 8 = 8 5 * 1 = 5
added together = 7053
156158
Watch
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Do this one
20458
106110
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Binary hex octal
If you can count from 1 to 15 in binary you have it made
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
1111
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Binary to hexadecimal and hex to binary 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 1101011110 to hex
Binary Hexadecimal
11 0101 1110
3 5 E
35E16
Hex Binary
28D1
10 1000110100012
Watch
Write this down the side of your paper.
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Practice Hex Binary Hex
Convert E5816 to Binary111001011000
Convert 110010110 to Hexadecimal196
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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
10110011
10 110 011
263
Octal to binary
451
100 101 001
100101001 Watch
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Practice Octal Binary Octal
Convert 3078 to Binary11000111
Convert 110010110 to Octal646
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octal to hex and hex to octal.
Convert to binary, regroup and convert to other base.
Octal to binary to hex4518
100 101 001
100101001
1 0010 100112916
Watch
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Practice Octal Hex
Convert 3078 to Hex11 000 111 first in binary110001111100 0111 divide into groups of 4 12 7C716
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Practice Hex Octal
Convert 2B1D16 to Octal10 1011 0001 1101 first in binary10101100011101 10 101 100 011 101 divide into groups of 3 2 5 4 3 5254358
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The End