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# Serial Multipliers Using Multi-bit Adders

IP.com Disclosure Number: IPCOM000121286D
Original Publication Date: 1991-Aug-01
Included in the Prior Art Database: 2005-Apr-03
Document File: 5 page(s) / 163K

IBM

## Related People

Gyllenhammer, CR: AUTHOR [+2]

## Abstract

The shift and add method of multiplying is a very simple method. When a binary number is shifted to the left by one place, the new number = (original number)x2.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 41% of the total text.

The shift and add method of multiplying is a very simple
method.  When a binary number is shifted to the left by one place,
the new number = (original number)x2.

By using this fact, a number can be multiplied by any other
number by adding a series of shifted original values.

For example, a "Shift and Add" multiplier would multiply the
binary number '0110'b by the binary number '111'b in the following
manner:
.   the binary value '0110'b would be added to '01100'b to
yield the partial product '10010'b
.   the partial product '10010'b would be added to '011000'b
to yield the final product '101010'b.

This method uses very little logic but takes multiple cycles to
perform the multiplication operation.

The logic array multiplier is a more complicated method of
producing a product.

This method works similar to a memory array.  All possible
multiplication combinations are predetermined.  The number and the
multiplier are then used as address lines to access the location that
has the proper product.

This method is very fast but uses a large amount of logic.

The main element in constructing a serial multiplier is the use

The standard logic ADDER takes two inputs and generates an
output that is really a binary encode of the number of input signals
that are active.

The multi-bit adder is just an extension of this concept.  It
will take any number of input signals and produce the binary encode
of the number of input signals that are active.

For example, a 5-bit multi-bit would need 3 outputs. If 4 of
the 5 inputs were active, the binary value '100'b would be produced
on the 3 outputs.

The serial multiplier uses the shift and add concept, but the
serial multiplier does all the shift and add function in one

together.  A screen of AND gates are placed before the multi-bit
adders to remove the shifted values that are not to be added.

For example, to multiply the 4-bit binary number 'ABCD'b by a
3-bit number 'EFG'b, the multi-bit adders would have the ability to
add binary value '00ABCD'b to '0ABCD0'b to 'ABCD00'b.
.   The value '00ABCD'b would be screened out of the serial
multiplier if the value of 'G' in the multiplier number was a zero.
.   The value '0ABCD0'b would be screened out of the serial
multiplier if the value of 'F' in the multiplier number was a zero.
.   The value 'ABCD00'b would be screened out of the serial
multiplier if the value of 'E' in the multiplier number was a zero.

This type of screening system will generate the proper product.

Placing values in this example, let us say the binary number
'0011'b is to be multiplied by '101...