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 4-digit numbers is as follow:
Eg. 910 * 810
910= 10012
810 =10002
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 4-bit 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 4210 by 610 using binary division
Answer:
4210 =1010102
610 =1102
Hence quotient is 1112 and remainder is 0002
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 F016with 4516
F016=1111 00002
4516=0100 01012
And we can perform the multiplication in binary form.