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Basic Computer Operation-Arithmetic Operations-Multiplication

Data is operated with the use of the instructions of the arithmetic in the digital computer. Data is operated to generate outcomes required for the problems of the computing to the provided solution. The basic arithmetic operations are mainly divided into four types, these are – addition, subtraction, multiplication, and division. To implement the arithmetic operation-multiplication there is a discrete section in the digital computer known as an arithmetic processing unit. The instructions of arithmetic operation are executed usually on decimal and binary data. Fixed numbers are used to signify fractions or integers.

Arithmetic operation

The Arithmetic operation is a set of 4 basic arithmetic operations to be accomplished to add, subtract, divide, and multiply more than two extents. Four basic rules are included in the arithmetic operation that are addition, subtraction, division, and multiplication. For these arithmetic operations, specific symbols are used for each. These are:

  • Addition 
  • Subtraction 
  • Division    
  • Multiplication 

Addition

It is the basic skill of mathematics that calculates and finds the total of more than two numbers or in other words, we can say that adds two or more things together. The addition is represented through the ‘+’ symbol.

Subtraction

This arithmetic operation expresses the difference between two numbers. The subtraction is represented through the ‘-’ symbol.

Division

The division is the process of something dividing into equal groups and parts. In the four arithmetic operations, the division is the one that provides a fair answer of equal sharing. It is the inverse process of multiplication.

Multiplication

The addition is performed, again and again, this process is represented as multiplication. The multiplication is represented through the ‘*’ symbol. As the arithmetic operation, multiplication supports finding the final result when a number itself is repeated numerous times. In the process of multiplication, the terms multiplier and multiplicand are used. The product term is utilised for the multiplication result of the multiplier and multiplicand.

Multiplication process

There are several distinct methods of arithmetic operation-multiplication, but at the base most significantly, utilise some lookup table’ sort. This is the same method that at the school children were taught at the multiplication table.

In the binary method, there are 8-bit (256 bytes) outcomes from multiplying two 4-bit binary numbers. 256 byte is an expedient size for the lookup table determined with all results as possible. so that a CPU could multiply numbers of two 8 bit through breaking into numbers of two 4 bit. After that look for the 4×4 four partial products and add them with fluctuating offsets of 4 bit, to generate the product of 16 bit. This is a very quick process. A larger expired CPU can have enough space to make a larger lookup table. The 8×8 multiplication table becomes unbearably large. It also is conceivable in microcode to do with the traditional algorithm of shift-and-add, but this algorithm is very slow.

Multiplication algorithm

In the starting, the B is the multiplicand and a Q is the multiplier. The signs of their corresponding are in the B and Qs respectively. We compare the A’s and Q’s signs and set the corresponding product sign, then a product with double length will be stored in the A and Q registers. A and E registers are cleared and the SC, a sequence counter is set for several multiplier bits. Then a multiplicand should be kept with their sign, the word’s 1 bit will be engaged through the sign, and the with the n-1 bits will consist of the magnitude.

Now, the multiplier’s low order bit is tested in the Qn. If the multiplier is 1, the B (multiplicand) is added to A (partial product), otherwise 0. Q register is shifted from the novel partial product once to the right. The sequence counter SC is decreased through the 1 and checks its new value. The SC  0, the process is repeated again and again and forms a novel partial product. When SC=0, the process is stopped.

Booth’s algorithm

  •       The algorithm provides a process for binary integers multiplying in the complement representation of signed-2.
  •       It activates on the circumstance that 0 strings in the multiplier no addition is required but just shifting, but 1’s string in the multiplier from bit 2k to 2m weight could be preserved as 2k+1 – 2m.
  •       For instance, the number of binary 001110 (+14) has a 1’s string from 23 to 21 (k=3, m=1). The number could be signified as 2k+1 – 2m. = 24 – 21 = 16 – 2 = 14. Consequently, the  multiplication, where M = multiplicand and 14 = multiplier, could be completed as  .
  •       Therefore the product could be attained through the binary multiplicand M shifting 4-times to the left and subtracting M once shifted left.

Conclusion

This article represents the brief knowledge about computer arithmetic operation. The basic arithmetic operations are mainly divided into four types, these are – addition, subtraction, multiplication, and division. The Arithmetic operation is a set of 4 basic arithmetic operations to be accomplished to add, subtract, divide, and multiply more than two extents. As the arithmetic operation multiplication supports finding the final result when a number itself is repeated numerous times. In the process of multiplication, the terms multiplier and multiplicand are used. The product term is utilised for the multiplication result of the multiplier and multiplicand. There are several distinct methods of multiplication, but at the base most significantly, utilise some lookup table’ sort.