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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.
The rules for binary subtraction:
X Y X + Y 0 (10) (10) (10) _____ Borrow
0 0 (borrow 1, so that 10 – 1 = 1) – 1 0 0 0
0 – 0 = 0
1
0 – 1 = 1
0
Prime (Ver. 2.2)-VII For example, let us subtract the binary number (111) from (1000) . 0 1
1
1
1
0 0
1
1 – 0 = 1
0
1 – 1 = 0
1
1
Binary Multiplication 2 2
Binary numbers are multiplied in the same manner as decimal numbers. When two binary
12 numbers are multiplied, for each digit of the second number, the product of that digit of
the first binary number is calculated. Then it is shifted leftwards so that its rightmost digit
lines up with the digit in second number that was used. The sum of all these partial products
gives the result. The following rules are followed to multiply two binary numbers.
X Y X × Y 1 0 1 0
0 0 0 × 0 = 0 1 0 1
0 1 0 × 1 = 0 1 0 1 0
1 0 1 × 0 = 0 0 0 0 0 ×
1 1 1 × 1 = 1 1 0 1 0 × ×
1 1 0 0 1 0
For example, let us multiply (1010) by (101) .
2
2
21 st
Century #Critical Thinking
Skills
Warm Convert the following numbers and fill in the blanks:
Up! a. 142 in octal is equal to _________ in decimal.
b. 4A4 in hexadecimal is equal to _________ in decimal.
c. 1011011011 in binary is equal to _________ in decimal.
Let's Revisit
• A number system is simply a manner of counting.
• There are four types of number systems: Decimal, Octal, Binary and Hexadecimals.
• We can perform the different types of mathematical operations on binary numbers.

