Binary 4×4 Multiplier Logic
A binary 4×4 multiplier is a device that performs the 4-bit by 4-bit binary multiply
algorithm. The following is an example of such algorithm:
Note that in binary multiplication, the process involves shifting the multiplicand, and adding the
shifted multiplicand or zero. Each bit of the multiplier determines whether a 0 is added or a shifter
version of the multiplicand (0 implies zero added, 1 implies shifted multiplicand added). Thus, we can
infer a basic shift-and-add algorithm to implement unsigned binary multiplication.
In general, the logic is described as:
Figure 1. Binary 4×4 multiplier logic
The 4x4 binary multiplier circuit has 8 inputs and 8 outputs.
One way of designing a multiplication circuit is through designing a circuit that would implement an
array addition. This method would make use of half and full adders making it a very modular design
approach. .
. Figure below illustrates how this algorithm would apply to perform a multiplication between 2 4-bits
unsigned integer multiplication.
4*4 Multiplier
Figure 12 shows a block diagram for a basic 4 bit multiplier unit.
A [4 bits]
4-bit Unsigned
Multiplier
B [4 bits]
+
C
Y7
Y [8 bits]
A3
A2
A1
A0
Inputs
x
B3
B2
B1
B0
C
B0 x A3 B0 x A2 B0 x A1 B0 x A0
+
B1 x A3 B1 x A2 B1 x A1 B1 x A0
C
sum
sum
sum
sum
+
B2 x A3 B2 x A2 B2 x A1 B2 x A0
Internal Signals
C
sum
sum
sum
sum
B3 x A3 B3 x A2 B3 x A1 B3 x A0
sum
Y6
A [4 bits]
B [4 bits]
sum
Y5
8 bits
Transmission
Gate
sum
Y4
Ain [4 bits]
Bin [4 bits]
sum
Y3
Y2
Y1
Y0
4-bit Unsigned
Multiplier
Y in [8 bits]
Inverter
Clk ‘
Clk
Outputs
8 bits
Transmission
Gate
Y [8 bits]