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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
For example, let us subtract the binary number (111) from (1000) .
2 2
1 1
0 (10) (10) (10) _____
Borrow
1 0 0 0
– 1 1 1
0 0 0 1
Modern day binary number system was invented by Gottfried Lebiniz in 1679.
Let's REFRESH
A number system is a collection of numbers used to describe various quantities.
The decimal number system consists of ten digits from 0 to 9.
The binary number system consists of two digits 0s and 1s.
The octal number system is used as a shorthand representation of long binary numbers.
The hexadecimal number system consists of 16 digits from 0 to 9 and A to F.
exercise
A. Tick ( ) the correct option.
1. Which of the following is called the right-most digit before the fractional point in the binary number
system?
(i) MSD (ii) LSD
(iii) BSD (iv) None of these
Number System 13

