Linux with Operating System Concepts

i
2
i
Abbreviation and Meaning
10
1024
1K (kilo), approximately 1 thousand
20
1048576
1M (meg or mega), approximately 1 million
30
1073741824
1G (gig or giga), approximately 1 billion
40
1099511627776
1T (tera), approximately 1 trillion
50
1125899906842624
1P (peta), approximately 1 quadrillion
60
1152921504606846976
1E (exa), approximately 1 quintillion

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Appendix
Let us try an example. We will convert 81 from decimal to binary. The steps are shown 
in Table A.3. Here, we see 81 is divided by 2 yielding a quotient of 40 and a remainder of 
1 (81/2 
=
40 and 1/2, the remainder then is 1). We record both values. Now we divide the 
quotient, 40, by 2, which gives us a quotient of 20 and a remainder of 0 (40/2 
=
20 and 0/2, 
so there is no remainder). 20/2 
=
10 and 0/2 (quotient of 10, remainder of 0). 10/2 
=
5 and 
0/2 (quotient of 5, remainder of 0). 5/2 
=
2 and 1/2 (quotient of 2, remainder of 1). 2/2 
=
1 
and 0/2 (quotient of 1, remainder of 0). Finally, 1/2 
=
0 and 1/2 (quotient of 0, remainder 
of 1). Our binary equivalent to 81 then is the collection of remainders from the end of the 
process to the beginning, or 1010001
2
.
Note in our example from Table A.3 our result is a 7-bit number, 1010001
2
. If we wanted 
to store this in 8 bits, we would add a leading 0 giving us 01010001
2
. Given our binary 
result, we can confirm that it is correct by converting it back to decimal: 01010001
2
=
64 
+
16 
+
1 
=
81.
The other approach to convert decimal to binary is in essence the process of converting 
binary to decimal in reverse. Rather than adding up the powers of 2 indicated by the 1 bits 
in the binary number, we must determine which powers of 2 make up the decimal number 
and record those bits as 1s.
For instance, 81 is the result of 64 
+
16 
+
1 
=
0*2
7
+
1*2
6
+
0*2
5
+
1*2
4
+
0*2
3
+
0*2
2
+
0*
2
1
+
1*2
0
=
01010001
2
. To solve the problem through subtraction, we determine the largest 
power of 2 that we can subtract from the original number. With 8 bit numbers, the largest 
power of 2 will be 128. Let us practice a few, starting with 219.
• Largest power of 2 less than or equal to 219 is 128
• 219 
−
128 
=
91
• Largest power of 2 less than or equal to 91 is 64
• 91 
−
64 
=
27
• Largest power of 2 less than or equal to 27 is 16
• 27 
−
16 
=
11
• Largest power of 2 less than or equal to 11 is 8
• 11 
−
8 
=
3
TABLE A.3 
Example Converting 81 to Binary