This document provides an overview of number conversion between different numeric systems including binary, decimal, hexadecimal, and octal. It discusses the techniques for converting between each system such as multiplying or dividing place values and keeping track of remainders. Conversion examples are also provided such as converting the binary number 101011 to the decimal 43.
4. System Base Symbols
Used by Used in
humans computers
? ?
Decimal 10 0, 1, โฆ 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, โฆ 7 No No
Hexade
cimal
16 0, 1, โฆ
9,
No No
A, B, โฆ
F
Common Number Systems
6. โข Technique
โMultiply each bit by 2n, where n is the
โweightโ of the bit.
โThe weight is the position of the bit,
starting from 0 on the right.
โAdd the results.
Binary to Decimal
7. (101011)2 1
2
0
=> 1 x 20 =
1 x 21 =
0 x 22 = 0
1 x 23 = 8
0 x 24 =
1 x 25 = 32
(43)10
Bit โ0โ
EXAMPLE
18. Octal to Decimal
Technique
โข Multiply each bit by 8n, where n is
the โweightโ of the bit.
โข The weight is the position of the
bit, starting from 0 on the right.
โข Add the results
19. 7248 =>4 x
2 x
7 x
= 4
= 16
= 448
80
81
82
(468)10
30. Technique
Multiply each bit by 16n, where n is the
โweightโ of the bit
The weight is the position of the bit, starting
from 0on the right
Add the results
31.
32. ABC16 => C x 160 = 12 x 1 = 12
B x 161 = 11 x 16 = 176
A x 162 = 10 x 256 = 2560
274810
Example
