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Octal to Decimal Conversion
Similar to binary number, you can convert an octal number into decimal number by multiplying
each digit of the number with the increasing powers of 8 starting from right-hand side.
For example,
Example 1: Convert (37) into decimal. Example 2: Convert (467) into decimal.
8
8
1
0
(37) = 3 × 8 + 7 × 8 (467) = 4 × 8² + 6 × 8¹ + 7 × 8 0
8
8
= 24 + 7 = 4 × 64 + 6 × 8 + 7 × 1
(37) = (31) (467) = (311) 10 NUMBER SYSTEM
10
8
8
Hexadecimal to Decimal Conversion
You can convert a hexadecimal number into decimal number by multiplying each digit of the
number with the increasing powers of 16 starting from right-hand side. For example,
Example 1: Convert (3B) into decimal. Example 2: Convert (3A4) into decimal. 11
16
16
1
3B = 3 × 16 + 11 × 16 (3A4) = 3 × 16² +10 × 16¹ + 4 × 16 0
0
16
16
= 48 + 11 = 768 + 160 + 4
(3B) = (59) (3A4) = (932) 10
16
10
16
Operations on Binary Numbers
Similar to mathematics, a computer system can perform different operations on binary
numbers like addition, subtraction, multiplication, and division.
Binary Addition
Binary addition is similar to the addition of decimal numbers. When the value of addition
exceeds the value 1, say 10 or 11, then 1 is carried over to the left of the current position.
The rules for adding two binary digits are given below:
X Y X + Y
0 0 0 + 0 = 0 1 1 1 1 1 _____ Carry bits
0 1 0 + 1 = 1 1 0 1 1 1 1
1 0 1 + 0 = 1 + 1 0 1 1 1
1 1 1 + 1 = 10 (carry 1) 1 0 0 0 1 1 0
For example, let us add the binary numbers (101111) and (10111) .
2
2
Binary Subtraction
In binary subtraction, binary number of lower value is subtracted from the binary number
of higher value. The following table explains the subtraction of digit Y from digit X.

