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Example 1: Convert (1111) to decimal number.
2
1
2
3
0
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2
= 8 + 4 + 2 + 1
= 15
(1111) = (15) 10
2
Example 2: Convert (10111) to decimal number.
2
4
1
2
3
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 0
= 16 + 0 + 4 + 2 + 1
= 23
(10111) = (23) 10
2

Topic Flashback 21 st Century #Critical Thinking
Skills
Convert the binary number 1000 into decimal.

OPERATIONS ON BINARY NUMBERS

Let's learn the basic operations on binary numbers.

Binary Addition

Binary addition is similar to adding 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)

Number Systems & Binary in Computing and AI 73