Difference between revisions of "Binary system"

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To increment a binary number, follow this rule:
 
To increment a binary number, follow this rule:
  
−
1. Current digit is the end digit
+
1. Current digit is the end digit
−
2. Change the current digit
+
2. Change the current digit
−
3. If current digit = 1
+
3. If current digit = 1
−
4. Then:
+
4. Then:
−
4a.Shift current digits to away from the end digit
+
  4a.Shift current digits to away from the end digit
−
4b.Goto step 2
+
  4b.Goto step 2
−
5: Else:
+
5: Else:
−
5a:You're done.
+
  5a:You're done.
  
 
A more concrete example can be found here:
 
A more concrete example can be found here:
Line 16: Line 16:
  
 
The first 16 binary digits:
 
The first 16 binary digits:
−
:0:0
+
{|style="text-align:center"
−
:1:1
+
!Decimal!!Colspan=2 |Binary
−
:10:2
+
|-
−
:11:3
+
|width=50px|0
−
:100:4
+
|width=50px align="right"|0
−
:101:5
+
|width=10px| 
−
:110:6
+
|-
−
:111:7
+
|1
−
:1000:8
+
|align="right"|1
−
:1001:9
+
|-
−
:1010:10
+
|2
−
:1011:11
+
|align="right"|10
−
:1100:12
+
|-
−
:1101:13
+
|3
−
:1110:14
+
|align="right"|11
−
:1111:15
+
|-
−
:10000:16
+
|4
 +
|align="right"|100
 +
|-
 +
|5
 +
|align="right"|101
 +
|-
 +
|6
 +
|align="right"|110
 +
|-
 +
|7
 +
|align="right"|111
 +
|-
 +
|8
 +
|align="right"|1000
 +
|-
 +
|9
 +
|align="right"|1001
 +
|-
 +
|10
 +
|align="right"|1010
 +
|-
 +
|11
 +
|align="right"|1011
 +
|-
 +
|12
 +
|align="right"|1100
 +
|-
 +
|13
 +
|align="right"|1101
 +
|-
 +
|14
 +
|align="right"|1110
 +
|-
 +
|15
 +
|align="right"|1111
 +
|-
 +
|16
 +
|align="right"|10000
 +
|}
  
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]

Revision as of 17:06, July 14, 2007

The binary system is a way of representing numbers in base 2, i.e. using only the digits 0 and 1. While it is impractical for human use, it is the mainstay of modern computing.

To increment a binary number, follow this rule:

1. Current digit is the end digit
2. Change the current digit
3. If current digit = 1
4. Then:
 4a.Shift current digits to away from the end digit
 4b.Goto step 2
5: Else:
 5a:You're done.

A more concrete example can be found here: http://woodgears.ca/marbleadd/index.html

The first 16 binary digits:

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111
16 10000