Now a days, I am preparing for ZCE. Bitwise operation was something which was a headache for me. So when I was searching for some good tutorial on internet. I got this. Its really a very nice tutorial about the Bitwise operations in PHP and Bits, Bytes, and Binary Math. So I thought to share with you techies. Enjoy!
BINARY MATH INTRODUCTION
The bitwise operators utilize something called Binary Math. If you already know binary math, skip ahead. Binary math is a BASE 2 numbering system, where as our normal everyday numbering system is a BASE 10 system. Think back to elementary school where we learned numbers this way…
Think of the number 4768. Thats a normal everyday decimal number.
If you write that out full its 4 THOUSAND, 7 HUNDRED, 6 TENS, 8 ONES
or (4 * 103) + (7 * 102) + (6 * 101) + (8 * 100) = 4768
The BASE 2 system has the same concept however it goes by 2′s instead of 10s. So you can only have a value of 0 or 1. Lets look at a binary number
00101101 = (0 * 27) + (0 * 26) + (1 * 25) + (0 * 24) + (1 * 23) + (1 * 22) + (0 * 21) + (1 * 20) = 32 + 8 + 4 + 1 = 45
Wow thats alot of math. Lets break it down piece by piece starting with the first parentheses.
(0 * 27) which means 0 TIMES 2 to the POWER of 7 or 0 * ( 2 * 2 * 2 * 2 * 2 * 2 * 2) which basically comes out to 0 * 128 which equals 0 (0 times anything is 0)
so going down our binary number we can see it calculates like this:
0 – (0 * 128) = 0
0 – (0 * 64) = 0
1 – (1 * 32) = 32
0 – (0 * 16) = 0
1 – (1 * 8 ) = 8
1 – (1 * 4) = 4
0 – (0 * 2) = 0
1 – (1 * 1) = 1
so add those all up together 32 + 8 + 4 + 1 and you get 45
Bits, Bytes, and Binary Math
What is a bit? A bit is a representation of 1 or 0. Basically OFF and ON. Why do computers use such simple math? Well computers process with electric current so if the current is over a certain level the computer considers that to mean ON or 1 and if it is under that level it is set to OFF or 0.
What is a byte? A byte is made up of 8 bits and the highest value of a byte is 255, which would mean every bit is set. We will look at why a byte’s maximum value is 255 in just a second.
What does a byte look like?
| 1 Byte ( 8 bits ) | ||||||||||
| Place Value |
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
||
That is a representation of 1 Byte.
The “Place Value” column represents the math we did doing 2 to the power of 7,6,5,4,3,2,1,0
So if all bits are set and the value = 255 my byte would look like this
|
1 Byte ( 8 bits )
|
||||||||||
| Place Value |
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
||
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
1
|
=
|
255 | |
How do we get 255?
Lets take it right to left and add up all those values together
1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255
What would the number 22 look like?
|
1 Byte ( 8 bits )
|
||||||||||
| Place Value |
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
||
|
0
|
0
|
0
|
1
|
0
|
1
|
1
|
0
|
=
|
22
|
|
2 + 4 + 16 = 22
Lets look at some other examples of decimal to binary, the ones on the end try for yourself.
43 = 00101011
4 = 00000100
230 = ?
65 = ?
31 = ?
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