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Digital Electronics
NUMBER SYSTEM
INTRODUCTION
DECIMAL & BINARY SYSTEM
OCTAL & HEXADECIMAL SYSTEM
DECIMAL to BINARY CONVERSION
DECIMAL to OCTAL & HEXADECIMAL
BINARY to OCTAL & HEXADECIMAL and vice versa
ADDITION
SUBTRACTION
MULTIPLICATION & DIVISON
COMPLIMENTS
SUBTRACTION using r's COMPLIMENTS
BINARY CODES
BOOLEAN ALGEBRA
K MAPS
COMBINATIONAL CKT
SEQUENTIAL CIRCUITS
TIMING CIRCUITS

 

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 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.

 

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