Page 14 - Computer_Genius_v2.1_C7_flipbook
P. 14
-1
-2
0
2
1
101.101 = 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 -3
= 1 × 4 + 0 + 1 × 1 + ½ + 0 + 1/8
= 4 + 1 + 0.5 + 0.125
= 5.625
( 101.101) = (5.625)
2 10
Critical Thinking
Quest
1. Convert the binary number 1000.10 into decimal.
2. Convert decimal number 30 into binary.
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
1 1 1 1 1 _____ Carry bits
0 0 0 + 0 = 0 1 0 1 1 1 1
0 1 0 + 1 = 1 + 1 0 1 1 1
1 0 1 + 0 = 1 1 0 0 0 1 1 0
1 1 1 + 1 = 10 (carry 1)
For example, let us add the binary numbers (101111) and (10111) .
2 2
Binary Subtraction
In binary subtraction, binary number of lower value is subtracted from the binary number of higher
value. The given table explains the subtraction of digit Y from digit X.
12 Computer Genius (V2.1)-VII

