Page 12 - TP-Play_V-2.0_Book-8
P. 12
= 1 × 4 + 0 + 1 × 1 + ½ + 0 + 1/8
= 4 + 1 + 0.5 + 0.125
= 5.625
(101.101) = (5.625)
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. 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
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. If Y is greater
than X, then 1 is borrowed from the next position. When the binary digit 0 borrows 1 from the
next most significant digit, it becomes 10.
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 Play (Ver. 2.0)-VIII

