Simplifying Binary Representation

Class Exercise 1 Solution

28.37510 = 11100.0112

1100111.1012 = 103.62510




University of KwaZulu-Natal 2-1
ENEL2EBH2 - 2010

,Simplifying Binary Representation
As the magnitude of numbers increase, binary
representation becomes cumbersome. Base 2 is a
natural system for binary machines like computers
but is tedious for humans.

In order to read binary numbers easily we use base 8
(octal number system) and base 16 (hexadecimal).

Since binary, octal and hexadecimal numbers have
multiple-of-2 bases, conversion from one number
system to the other is simple. In conversion to octal,
just group binary digits into 3s starting from the
binary point to the left and to the right. Then convert
each group into the corresponding octal digits. Thus,
10110001101011.1111000001102 = 26153.74068.

University of KwaZulu-Natal 2-2
ENEL2EBH2 - 2010

, Simplifying Binary Representation
In conversion to hexadecimal, just group binary
digits into 4s starting from the binary point to the left
and to the right. Then convert each group into the
corresponding hexadecimal digits. Thus,
10110001101011.1111000001102 = 2C6B.F0616.
¾ The tables in the next slide summarize the
equivalence of binary values to octal and
hexadecimal values.




University of KwaZulu-Natal 2-3
ENEL2EBH2 - 2010