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Step 3 Add up all the resulting products. You will get your decimal number.
The following examples will help you to understand the conversion.
Example 1: Convert (1111) to decimal number.
2
1
2
3
0
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2
= 8 + 4 + 2 + 1
= 15
(1111) = (15)
2 10
Example 2: Convert (10111) to decimal number.
2
3
2
4
1
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 0
= 16 + 0 + 4 + 2 + 1
= 23
(10111) = (23)
2 10
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
= 3 × 8 + 7 × 8 0 = 4 × 8² + 6 × 8¹ + 7 × 8⁰
= 24 + 7 = 4 × 64 + 6 × 8 + 7 × 1
(37) = (31) (467) = (311)
8 10 8 10
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.
16 16
1
= 3 × 16 + 11 × 16 0 = 3 × 16² +10 × 16¹ + 4 × 16⁰
= 48 + 11 = 768 + 160 + 4
(3B) = (59) (3A4)₁₆ = (932)₁₀
16 10
OPERATIONS ON BINARY NUMBERS
Let's learn the basic operations on binary numbers.
12 Plus (Ver. 3.2)-VII

