MULTIPLICATION & DIVISION:
We similarly can apply the procedures of addition or subtraction during multiplication and division and get the results for multiplication and division of different numbering systems
MULTIPLICATION:
Procedure of multiplication is same as that of decimal
Generalized multiplication of two 4digit numbers is as follow:
Eg. 9_{10} * 8_{10}
9_{10}= 1001_{2}
8_{10} =1000_{2}
Similarly we can do it for fractional binary numbers; we just have to adjust binary point to the numbers of places equal to addition of numbers of places of the multiplicand and multiplier
If we implement the general multiplication method of two 4bit numbers then we need 16 AND gates to calculate those 16 terms of multiplication and also full adders to add the terms and the carries flying from one column to another as shown below:
DIVISON: Similar to multiplication we can do division as shown below:
Q Divide 42_{10} by 6_{10} using binary division
Answer:
42_{10 }=101010_{2}
6_{10} =110_{2}
Hence quotient is 111_{2} and remainder is 000_{2}
Division and multiplication for octal and hexadecimal number system:
We can convert the octal and hexadecimal numbers to binary and perform the multiplication and division as it would be very cumbersome to do it by keeping the numbers in their given form
Q Multiply F0_{16}with 45_{16}
F0_{16}=1111 0000_{2}
45_{16}=0100 0101_{2}
And we can perform the multiplication in binary form.
