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Example 3: Convert (101.101) to decimal number.
2
Position 2 1 0 –1 –2 –3
Face value 1 0 1 • 1 0 1
Weights 2 2 2 1 2 0 2 –1 2 –2 2 –3
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) 10
2
Double Tap Century #Critical thinking
21 st
Skills
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 1 1 + 1 = 10 (carry 1) 1 0 0 0 1 1 0
For example, let us add the binary numbers (101111) and (10111) .
2
2
#Number System 15

