Different Base systems

Binary Numbers:
The binary system contains only two values in the
allowed coefficients (0 and 1).
• The binary system uses powers of 2 as the
multipliers for the coefficients.
• For example, we can represent the binary number
10111.01 as:
– 1 X 24 + 0 X 23 + 1 X 22 + 1 X 21 + 1 X 20 + 0 X 2-1 + 1 X 2-2 = 23.25
Octal Numbers:

The octal number system is a base-8 system that
contains the coefficient values of 0 to 7.
• The octal system uses powers of 8 as the multipliers
for the coefficients.
• For example, we can represent the octal number
72032 as:
7 X 84 + 2 X 83 + 0 X 82 + 3 X 81 + 2 X 80 = (29722)10
Hexadecimal Numbers:

The hexadecimal number system is a base-16 system
that contains the coefficient values of 0 to 9 and A to
F. The letters A through F represent the coefficient
values of 10, 11, 12, 13, 14, and 15, respectively.
• The hexadecimal system uses powers of 16 as the
multipliers for the coefficients.
• For example, we can represent the hexadecimal
number C34D as:
– 12 X 163 + 3 X 162 + 4 X 161 + 13 X 160 = (49997)10
Conversion From any base to Decimal:

Conversion of a number in base r to decimal is done
by expanding the number in a power series and
adding all the terms.
• For example, (C34D)16 is converted to decimal:
12 X 163 + 3 X 162 + 4 X 161 + 13 X 160 = (49997)10
• (11010.11)2 is converted to decimal:
1 X 24 + 1 X 23 + 0 X 22 + 1 X 21 + 0 X 20 + 1 X 2-1 + 1 X 2-2 = 26.75