Binary

From Compsci1

Revision as of 20:17, 1 October 2006 (view source) Admin (Talk | contribs) ← Previous diff		Current revision as of 20:31, 1 October 2006 (view source) Admin (Talk | contribs) (→Rules of Binary Addition)
(2 intermediate revisions not shown)
Line 10:		Line 10:
	1 + 1 = 0, and carry 1 to the next more significant bit		1 + 1 = 0, and carry 1 to the next more significant bit
		+
	For example,		For example,
	00011010 + 00001100 = 00100110		00011010 + 00001100 = 00100110
-	1  1   carries	+	1  1                     carries
-	0  0  0  1  1  0  1  0    =    26(base 10)	+	0  0  0  1  1  0  1  0    =    26<sub>(base 10)</sub>
-	0  0  0  0  1  1  0  0    =    12(base 10)	+	0  0  0  0  1  1  0  0    =    12<sub>(base 10) </sub>
	+		+
-	<nowiki>--------------------------------------------------------------------------------</nowiki>	+	--------------------------------------------------------------------------------
-	0  0  1  0  0  1  1  0    =    38(base 10)	+	0  0  1  0  0  1  1  0    =    38<sub>(base 10) </sub>
Line 31:		Line 32:
	00010011 + 00111110 = 01010001		00010011 + 00111110 = 01010001
-	1  1  1  1  1   carries	+	1  1  1  1  1               carries
-	0  0  0  1  0  0  1  1    =    19(base 10)	+	0  0  0  1  0  0  1  1    =    19<sub>(base 10) </sub>
-	0  0  1  1  1  1  1  0    =    62(base 10)	+	0  0  1  1  1  1  1  0    =    62<sub>(base 10) </sub>
		+	+
-	+ <nowiki>----------------------------------------------------------------------</nowiki>	+	----------------------------------------------------------------------
-	0  1  0  1  0  0  0  1    =    81(base 10)	+	0  1  0  1  0  0  0  1    =    81<sub>(base 10)</sub>
-		+
	==Rules of Binary Subtraction==		==Rules of Binary Subtraction==
	0 - 0 = 0		0 - 0 = 0
		+
	0 - 1 = 1, and borrow 1 from the next more significant bit		0 - 1 = 1, and borrow 1 from the next more significant bit
		+
	1 - 0 = 1		1 - 0 = 1
		+
	1 - 1 = 0		1 - 1 = 0
		+
	For example,		For example,
	00100101 - 00010001 = 00010100		00100101 - 00010001 = 00010100
-	0   borrows	+	0                       borrows
-	0  0  <strike>1</strike> <sup>1</sup>0  0  1  0  1    =    37(base 10)	+	0  0  <strike>1</strike> <sup>1</sup>0  0  1  0  1    =    37<sub>(base 10) </sub>
-	0  0  0  1  0  0  0  1    =    17(base 10)	+
-	--------------------------------------------------------------------------------	+	0  0  0  1  0  0  0  1    =    17<sub>(base 10)</sub>
-	0  0  0  1  0  1  0  0    =    20(base 10)	+
		+	-
		+
		+	-------------------------------------------------------------
		+
		+	0  0  0  1  0  1  0  0    =    20<sub>(base 10)</sub>
	00110011 - 00010110 = 00011101		00110011 - 00010110 = 00011101
-	0 10 1   borrows	+	0 <sup>1</sup>0  1                   borrows
-	0  0  1  1  0 10 1  1    =    51(base 10)	+
-	- 0  0  0  1  0  1  1  0    =    22(base 10)	+	0  0  <strike>1  1  0 </strike><sup>1</sup>0 1  1    =    51<sub>(base 10)</sub>
		+
		+	0  0  0  1  0  1  1  0    =    22<sub>(base 10)</sub>
		+
		+	-
	--------------------------------------------------------------------------------		--------------------------------------------------------------------------------
-	0  0  0  1  1  1  0  1    =    29(base 10)	+	0  0  0  1  1  1  0  1    =    29<sub>(base 10)</sub>

---

Current revision as of 20:31, 1 October 2006

a good resource on Binary

Rules of Binary Addition

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0, and carry 1 to the next more significant bit

For example,

00011010 + 00001100 = 00100110

      1  1                     carries 

0  0  0  1  1  0  1  0    =    26(base 10) 

0  0  0  0  1  1  0  0    =    12(base 10) 

+

---

0  0  1  0  0  1  1  0    =    38(base 10) 

00010011 + 00111110 = 01010001

   1  1  1  1  1               carries 

0  0  0  1  0  0  1  1    =    19(base 10) 

0  0  1  1  1  1  1  0    =    62(base 10) 

+

---

 0  1  0  1  0  0  0  1    =    81(base 10)

Rules of Binary Subtraction

0 - 0 = 0

0 - 1 = 1, and borrow 1 from the next more significant bit

1 - 0 = 1

1 - 1 = 0

For example,

00100101 - 00010001 = 00010100

      0                        borrows 

0  0  1 10  0  1  0  1    =    37(base 10) 

0  0  0  1  0  0  0  1    =    17(base 10) 

-

---

0  0  0  1  0  1  0  0    =    20(base 10) 

 

00110011 - 00010110 = 00011101

      0 10  1                   borrows 

0  0  1  1  0 10  1  1    =    51(base 10)

0  0  0  1  0  1  1  0    =    22(base 10) 

-

---

0  0  0  1  1  1  0  1    =    29(base 10)

Notes

Binary Number System

System Digits: 0 and 1

Bit (short for binary digit): A single binary digit

LSB (least significant bit): The rightmost bit

MSB (most significant bit): The leftmost bit

Upper Byte (or nybble): The right-hand byte (or nybble) of a pair

Lower Byte (or nybble): The left-hand byte (or nybble) of a pair

Binary Equivalents

1 Nybble (or nibble) = 4 bits

1 Byte = 2 nybbles = 8 bits

1 Kilobyte (KB) = 1024 bytes

1 Megabyte (MB) = 1024 kilobytes = 1,048,576 bytes

1 Gigabyte (GB) = 1024 megabytes = 1,073,741,824 bytes