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BINARY TO DECIMAL CONVERSION
To convert a binary number into a decimal number, follow these steps:
✶ Start from the right-most digit known as the LSD before the fractional point, and move
towards left.
✶ Multiply each digit by 2 raised to the power corresponding to its position. The powers of
2 start from 0 and increase to 1, 2, and so on as you move towards left.
✶ Add up all the resulting products. This sum gives you the decimal number.
The following examples will help you understand the conversion better.
Example 1: Convert (1111) to decimal number.
2
0
1
2
3
= 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
2
3
4
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
We can perform various operations on binary numbers. Let's discuss binary addition and binary
subtraction in detail.
Binary Addition
Binary addition is similar to decimal addition. When the value of addition exceeds 1 (e.g., sums
of 10 or 11), a carry is moved to the left of the current position. The rules for adding two binary
digits are given below:
Let us add the binary numbers
X Y X + Y (101111) and (10111) .
2 2
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
Binary Subtraction
In binary subtraction, the smaller binary number is subtracted from the larger one. The table
below illustrates how to subtract digit Y from digit X. If Y is greater than X, we borrow 1 from the
next higher position. When a binary digit of 0 borrows 1, it effectively becomes 2 (written as 10
in binary).
Number System 25

