Page 10 - Code Craft Computer-7

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. 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 0 – 1 = 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 Extra Bytes
1 0 0 0 Modern day binary

number system was
+ 1 1 1
invented by Gottfried
0 0 0 1 (1000) – (111) = (0001) 2 Leibniz in 1679.
2
2

Flashback Time

¨ 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.

Knowledge Check
OMR Sheet
A. Mark the correct response.
Use only blue/black ball
1. Which of the following is called the right-most digit before the pen to fill the circles. It
should be darkened
fractional point in the binary number system? completely and properly.
Wrong methods
a. MSD b. LSD
c. BSD d. None of these Correct method
2. What is the another name for Base 2?

a. Binary number system b. Decimal number system 1. a b c d
c. Hexadecimal number system d. Octal number system 2. a b c d

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