The document describes a binary multiplier, a digital device used for multiplying binary numbers known as multiplicand and multiplier, yielding a product. It explains the differences between manual binary multiplication and its digital implementation, emphasizing the need for modifications to ensure correct results when operating on partial products. Additionally, it outlines the necessary components for the datapath subsystem, including various registers and a parallel adder circuit.

1. BINARY
MULTIPLIER
ELDHO MV

2. Introduction
A binary multiplier is a combinational logic circuit or
digital device used for multiplying two binary
numbers. The two numbers are more specifically
known as multiplicand and multiplier and the result
is known as a product.
10/11/2020
B I N A R Y M U L T I P L I E R
2

3. multiplicand 1 1 0 1
multiplier 1 0 1 0
0 0 0 0 partial product 1
1 1 0 1 partial product 2
sum 1 1 0 1 0
0 0 0 0 partial product 3
sum 0 1 1 0 1 0
1 1 0 1 partial product 4
1 0 0 0 0 0 1 0
fig : manual multiplication algorithm

4. Digital implementation requires the following changes
 In manual working, we perform left shift on the subsequent partial product which is
yet to be formed , but this kind of anticipatory job is not done by a physically realizable
machine . A real machine can operate only on the existing operands but not on future results.
Hence, we shift the partial product already formed to the right by one bit and add the next
partial product in its normal position . This would produce the correct results as the reality
positions of the operands for additions are as they should be
 Instead of forming all the partial products and then adding, which would require
a large number of registers to store them , each partial product is added to register A
(accumulator) and shifted right . This job is repeated n times where n is the number of
bits in the multiplier.

5. 5
Datapath Subsystem for Binary Multiplier
• Register B to hold the multiplicand.
• Register Q to hold the multiplier.
• Register A, called the accumulator, to hold the cumulative sum of products.
• A parallel adder circuit.

6. ASM chart for a binary multiplier

7. 10/11/2020 7
BINARYMULTIPLIER
THANK YOU
ELDHO MV