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Example 1: Convert (1111) to a decimal number.
2
0
1
2
3
= 1 × 2 + 1 × 2 + 1 × 2 + 1 × 2
= 8 + 4 + 2 + 1
= 15
(1111) = (15)
2 10
Example 2: Convert (10111) to a decimal number.
2
1
4
2
3
= 1 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 1 × 2 0
= 16 + 0 + 4 + 2 + 1
= 23
(10111) = (23)
2 10
OPERATIONS ON BINARY NUMBERS
Binary Addition
Binary addition is like decimal addition. When the sum is more than 1, like when adding 10 or 11
in binary, you carry 1 over to the next position on the left. 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) 1 1 1 1 1 _____ Carry bits
1 0 1 1 1 1
For example, let us add the binary numbers (101111)
2 + 1 0 1 1 1
and (10111) .
2
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 subtracting two binary digits are given below:
X Y X – Y
0 0 0 – 0 = 0
0 – 1 = 1
0 1 1 1
(borrow 1, so that 10 – 1 = 1) _____
1 0 1 – 0 = 1 0 (10) (10) (10) Borrow
1 1 1 – 1 = 0 1 0 0 0
– 1 1 1
For example, let us subtract the binary number (111)
2
from (1000) . 0 0 0 1
2
Number System 25

