Prepared by: Ihsan Jabbar Lecture 2: Number Base Conversion
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Logic Design
Lecture 2
"Number Base Conversion"
A. Conversion from Decimal system to another systems (Binary,
Octal, Hexadecimal, …)
If the number has a fraction part, then the number is separated into
an integer part and fraction part and the conversion of each part
done separately.
The fraction part is multiplied by the base of the new system to give
an integer and fraction, the new fraction multiplied again to give a
new integer and new fraction. The process is continued until the
fraction becomes 0. The coefficients of a new number are obtained
from the integers.
Ex: Convert decimal to binary.
0.6875 * 2 1. 375 ( )
0.375 * 2 0. 75 ( )
0.75 * 2 1. 5 ( )
0.5 * 2 1. 0 ( )
=
Ex: Convert decimal to binary.
0.625 * 2 1. 25
0.25 * 2 0. 5
0.5 * 2 1. 0
=
