Page 222 - Concise Encyclopedia of Robotics

Numeration
0
1
2
3
2704.53816 = 2 10 + 7 10 + 0 10 + 4 10
2
3
5
1
4
+ 5 10 + 3 10 + 8 10 + 1 10 + 6 10
Binary numbers
The binary number system is a method of expressing numbers using
only the digits 0 and 1. It is sometimes called base 2, radix 2, or modulo 2.
The digit immediately to the left of the radix point is the “ones”digit. The
next digit to the left is a “twos” digit; after that comes the “fours” digit.
Moving farther to the left, the digits represent 8, 16, 32, 64, and so on,
doubling every time. To the right of the radix point, the value of each
digit is cut in half again and again, that is, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64,
and so on.
Consider an example using the decimal number 94:
1
0
94 = (4 10 ) + (9 10 )
In the binary number system the breakdown is
2
1
0
1011110 = (0 2 ) + (1 2 ) + (1 2 )
+ (1 2 ) + (1 2 ) + (0 2 ) + (1 2 )
4
3
6
5
When you work with a computer or calculator, you give it a decimal
number that is converted into binary form. The computer or calculator
does its operations with zeros and ones. When the process is complete,
the machine converts the result back into decimal form for display.
Octal and hexadecimal numbers
Another numbering scheme is the octal number system, which has eight
3
symbols, or 2 . Every digit is an element of the set {0, 1, 2, 3, 4, 5, 6, 7}.
Counting thus proceeds from 7 directly to 10, from 77 directly to 100,
from 777 directly to 1000, and so on.
Yet another scheme, commonly used in computer practice, is the
hexadecimal number system, so named because it has 16 symbols, or 2 . 4
These digits are the usual 0 through 9 plus six more, represented by A
through F, the first six letters of the alphabet. The digit set is {0, 1, 2, 3, 4,
5, 6, 7, 8, 9, A, B, C, D, E, F}.
Comparison of values
The table compares values in modulos of 10 (decimal), 2 (binary), 8
(octal), and 16 (hexadecimal), from decimal 0 through decimal 64.
In general, the larger the modulus, the smaller the numeral for a given
value.
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