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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
3
2
0
1
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2
= 8 + 4 + 2 + 1
= 15
(1111) = (15)
2 10
Example 2: Convert (10111)2 to decimal number.
4
2
3
1
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 + 2 0
= 16 + 0 + 4 + 2 + 1
= 23
(10111) = (23)
2 10
OPERATIONS ON BINARY NUMBERS
Let's learn the basic operations on binary numbers.
Binary Addition
Binary addition is similar to the addition of decimal numbers. In Binary Number System, 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
0 1 0 + 1 = 1
1 0 1 + 0 = 1
1 1 1 + 1 = 10 (carry 1)
For example, let us add the binary numbers (101111) and (10111) .
2
2
_____
1 1 1 1 1 Carry bits
1 0 1 1 1 1
+ 1 0 1 1 1
1 0 0 0 1 1 0
12 Play (Ver. 2.1)-VIII

