-
8/20/2019 Number Systems.pptx
1/52
Number Systems
-
8/20/2019 Number Systems.pptx
2/52
Common Number Systems
System Base Symbols
Used byhumans?
Used in PLC?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, … 7 No No
Hea!
"ecimal
1# 0, 1, … 9,
$, B, … %
No No
-
8/20/2019 Number Systems.pptx
3/52
&uantities'Countin( )1 o* +
Decimal Binary Octal Hexa-decimal
0 0 0 0
1 1 1 1
2 10 2 2
+ 11 + +
- 100 - -
. 101 . .# 110 # #
7 111 7 7
-
8/20/2019 Number Systems.pptx
4/52
&uantities'Countin( )2 o* +
Decimal Binary Octal Hexa-decimal
8 1000 10 8
9 1001 11 9
10 1010 12 $
11 1011 1+ B
12 1100 1- C
1+ 1101 1. D1- 1110 1# /
1. 1111 17 %
-
8/20/2019 Number Systems.pptx
5/52
&uantities'Countin( )+ o* +
Decimal Binary Octal Hexa-decimal
1# 10000 20 10
17 10001 21 11
18 10010 22 12
19 10011 2+ 1+
20 10100 2- 1-
21 10101 2. 1.22 10110 2# 1#
2+ 10111 27 17
/tc
-
8/20/2019 Number Systems.pptx
6/52
Conersion $mon( Bases
• 3e 4ossibilities5
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
7/52
Conersion $mon( Bases
• 3e 4ossibilities5
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
8/52
Binary to Decimal
• ec3ni6ue – ulti4ly eac3 bit by 2n, 3ere n is t3e
ei(3t:
o* t3e bit
–
3e ei(3t is t3e 4osition o* t3e bit, startin(*rom 0 on t3e
ri(3t
– $"" t3e results
-
8/20/2019 Number Systems.pptx
9/52
/am4le
1010112 => 1 x 20 = 1
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8
0 x 24 = 0
1 x 25 = 32
4310
Bit 0:
-
8/20/2019 Number Systems.pptx
10/52
Octal to Decimal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
11/52
Octal to Decimal
•ec3ni6ue – ulti4ly eac3 bit by 8n, 3ere n is t3e
ei(3t:
o* t3e bit
–
3e ei(3t is t3e 4osition o* t3e bit, startin(*rom 0 on t3e
ri(3t
– $"" t3e results
-
8/20/2019 Number Systems.pptx
12/52
/am4le
7248 => 4 x 80 = 4
2 x 81 = 16
7 x 82 = 448
46810
Bit 0:
-
8/20/2019 Number Systems.pptx
13/52
Hea"ecimal to Decimal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
14/52
Hea"ecimal to Decimal
•ec3ni6ue – ulti4ly eac3 bit by 1#n, 3ere n is t3e
ei(3t: o* t3e bit
–
3e ei(3t is t3e 4osition o* t3e bit, startin(*rom 0 on t3e
ri(3t
– $"" t3e results
-
8/20/2019 Number Systems.pptx
15/52
/am4le
ABC16 =>C x 160 = 12 x 1 = 12
B x 161 = 11 x 16 = 176
A x 162 = 10 x 256 = 2560
274810
-
8/20/2019 Number Systems.pptx
16/52
Decimal to Binary
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
17/52
Decimal to Binary
•ec3ni6ue – Dii"e by to, ;ee4 trac; o* t3e
remain"er
– %irst remain"er is bit 0 )
-
8/20/2019 Number Systems.pptx
18/52
/am4le
12510 = ?2 2 125 62 12
31 02
15 12
7 12
3 12
1 12
0 1
12510 = 1111101
2
-
8/20/2019 Number Systems.pptx
19/52
Octal to Binary
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
20/52
Octal to Binary
•ec3ni6ue – Conert eac3 octal "i(it to a +!bit
e6uialent
binary re4resentation
-
8/20/2019 Number Systems.pptx
21/52
/am4le
7058 = ?2
7 0 5
111 000 101
7058 = 111000101
2
-
8/20/2019 Number Systems.pptx
22/52
Hea"ecimal to Binary
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
23/52
Hea"ecimal to Binary
•ec3ni6ue – Conert eac3 3ea"ecimal "i(it to a -!bit
e6uialent binary re4resentation
-
8/20/2019 Number Systems.pptx
24/52
/am4le
10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 0001000010101111
2
-
8/20/2019 Number Systems.pptx
25/52
Decimal to Octal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
26/52
Decimal to Octal
•ec3ni6ue – Dii"e by 8
– =ee4 trac; o* t3e remain"er
-
8/20/2019 Number Systems.pptx
27/52
/am4le
123410 = ?8
8 1234
154 28
19 28
2 38
0 2
123410 = 2322
8
-
8/20/2019 Number Systems.pptx
28/52
Decimal to Hea"ecimal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
29/52
Decimal to Hea"ecimal
•ec3ni6ue – Dii"e by 1#
– =ee4 trac; o* t3e remain"er
-
8/20/2019 Number Systems.pptx
30/52
/am4le
123410 = ?16
123410 = 4D2
16
16 1234
77 216
4 13 = D16
0 4
-
8/20/2019 Number Systems.pptx
31/52
Binary to Octal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
32/52
Binary to Octal
•ec3ni6ue – >rou4 bits in t3rees, startin( on ri(3t
– Conert to octal "i(its
-
8/20/2019 Number Systems.pptx
33/52
/am4le
10110101112 = ?8
1 011 010 111
1 3 2 7
10110101112 = 1327
8
-
8/20/2019 Number Systems.pptx
34/52
Binary to Hea"ecimal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
35/52
Binary to Hea"ecimal
•ec3ni6ue – >rou4 bits in *ours, startin( on ri(3t
– Conert to 3ea"ecimal "i(its
-
8/20/2019 Number Systems.pptx
36/52
/am4le
10101110112 = ?16
10 1011 1011
2 B B
10101110112 = 2BB
16
-
8/20/2019 Number Systems.pptx
37/52
Octal to Hea"ecimal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
38/52
Octal to Hea"ecimal
•
ec3ni6ue – ?se binary as an interme"iary
-
8/20/2019 Number Systems.pptx
39/52
/am4le
10768 = ?16
1 0 7 6
001 000 111 110
2 3 E
10768 = 23E
16
-
8/20/2019 Number Systems.pptx
40/52
Hea"ecimal to Octal
Hea"ecimal
Decimal Octal
Binary
-
8/20/2019 Number Systems.pptx
41/52
Hea"ecimal to Octal
•
ec3ni6ue – ?se binary as an interme"iary
-
8/20/2019 Number Systems.pptx
42/52
/am4le
1F0C16 = ?8
1 F 0 C
0001 1111 0000 1100
1 7 4 1 4
1F0C16 = 17414
8
-
8/20/2019 Number Systems.pptx
43/52
Binary $""ition )1 o* 2
•
o 1!bit alues
44 +#!+8
$ B $ @ B
0 0 00 1 1
1 0 1
1 1 10to:
-
8/20/2019 Number Systems.pptx
44/52
Binary $""ition )2 o* 2
•
o n!bit alues – $"" in"ii"ual bits
– Aro4a(ate carries
–
/(,
10101 21
+ 11001 + 25
101110 46
11
-
8/20/2019 Number Systems.pptx
45/52
ulti4lication )1 o* +
•
Decimal )ust *or *un
35
x 105 175
000
35
3675
l i li i ) *
-
8/20/2019 Number Systems.pptx
46/52
ulti4lication )2 o* +
•
Binary, to 1!bit alues
$ B $ × B
0 0 0
0 1 0
1 0 0
1 1 1
l i li i )+ * +
-
8/20/2019 Number Systems.pptx
47/52
ulti4lication )+ o* +
•
Binary, to n!bit alues – $s it3 "ecimal alues
– /(,
1110
x 1011
1110
1110
0000 1110
10011010
% i
-
8/20/2019 Number Systems.pptx
48/52
%ractions
•
Binary to "ecimal
10.1011 => 1 x 2-4 = 0.0625
1 x 2-3 = 0.125
0 x 2-2 = 0.0
1 x 2-1 = 0.5
0 x 20 = 0.0
1 x 21 = 2.0
2.6875
% i
-
8/20/2019 Number Systems.pptx
49/52
%ractions
•
Decimal to binary
3.14579
.14579
x 2
0.29158
x 2
0.58316
x 2
1.16632
x 2
0.33264
x 2
0.66528
x 2
1.33056
etc.11.001001...
/ i C
-
8/20/2019 Number Systems.pptx
50/52
/ercise Conert
Dont use a calculatorE
Decimal Binary Octal
Hea!"ecimal
298
1011101
+07
C82
S;i4 anser $nser
/ i C
-
8/20/2019 Number Systems.pptx
51/52
/ercise Conert …
Decimal Binary Octal
Hea!"ecimal
298 11101110011… +.#+… 1DCC…
.812. 1011101 .#- .D
+109+7. 11000111 +07 +1C
12.07812. 110010000010 1--0- C82
$nser
-
8/20/2019 Number Systems.pptx
52/52
Thank you
![Wind Farm Electrical Systems.pptx [Read-Only]ewh.ieee.org/r3/atlanta/ias/Wind Farm Electrical Systems.pdf · 2010. 1. 19. · Wind Farm Electrical Systems. ... Maintenance Hoist](https://img.pdfslide.net/doc/110x75/6122e4b36403441c092ee882/wind-farm-electrical-read-onlyewhieeeorgr3atlantaiaswind-farm-electrical.jpg)
![2015 IBC Exit Systems.pptx [Read-Only] Associations... · 2015 IBC Exit Systems Section 1023.5 There shall be no penetrations or](https://img.pdfslide.net/doc/110x75/5ae7f6357f8b9a6d4f8ed3cd/2015-ibc-exit-read-only-associations2015-ibc-exit-systems-section-10235-there.jpg)
![Wind Farm Electrical Systems.pptx [Read-Only] Farm Electrical Systems.pdf · This adds to equipment and engineering costs and increases the substation footprint. Another ... Wind](https://img.pdfslide.net/doc/110x75/5a8a24657f8b9adb648bd06a/wind-farm-electrical-read-only-farm-electrical-systemspdfthis-adds-to-equipment.jpg)
![Wind Farm Electrical Systems.pptx [Read-Only] - IEEE Farm Electrical Systems.pdf · 20 miles of 34.5 kV XLPE 133% Insulated cable 50 MW ... Transformer 138 kV – 34.5 kV MVAR Losses](https://img.pdfslide.net/doc/110x75/5a8177b87f8b9a9d308d3e3d/wind-farm-electrical-read-only-ieee-farm-electrical-systemspdf20-miles-of-345.jpg)
![A Tale of Two Health Care Systems.pptx [Read-Only] · 2005 ‐ 8 2006 ‐ 5 2007 ‐ 2 ... RBRVS, COBRA, EMTALA, ... System‐Physician Alignment Essential ARP’s ACO’s Triple](https://img.pdfslide.net/doc/110x75/5f5b2da3b06ac91082167100/a-tale-of-two-health-care-read-only-2005-a-8-2006-a-5-2007-a-2-rbrvs.jpg)
