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Step 2 Add up all the resulting products. This sum gives you the decimal number.
Example: Convert (101001) to decimal number.
2
3
5
4
2
= 1 x 2 + 0 x 2 + 1 x 2 + 0 x 2 + 0 x 2 + 1 x 2 0
1
Sum of the products = 32 + 0 + 8 + 0 + 0 + 1 = 41
Therefore, (101001) = (41) 10
2
OPERATIONS ON BINARY NUMBERS
We can perform various operations on binary numbers. Let's discuss binary addition and binary
subtraction in detail.
BINARY ADDITION
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). 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
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). The rules for binary subtraction:
X Y X – Y
0 0 0 – 0 = 0
0 – 1 = 1
0 1
(borrow 1, so that 10 – 1 = 1)
1 0 1 – 0 = 1
1 1 1 – 1 = 0
12 Pro (V5.1)-VII

