# Design a 2-Bit Multiplier Circuit Using 4:1 MUX

A 2-Bit Multiplier Circuit is a combinational logic circuit that we use to multiply binary digits. Like the adder and the Subtractor, a multiplier is an arithmetic combinational logic circuit. It is also known as a binary multiplexer or a digital multiplier.

Binary multiplication works just like normal multiplication. There are four main rules that are quite simple to understand:

0×0 = 0
0×1 = 0
1×0 = 0
1×1 = 1

## Components Required

• IC-74153 4:1 Multiplexer (x2)
• IC-7486 EX-OR Gate
• IC-7408 AND Gate
• IC-7404 NOT Gate
• Single Pole 2-Way Switch (x4)
• 220 Resistor
• Green LED (x4)
• 5V Power Supply
• Wire

## About Parts of 2-Bit Multiplier Circuit

### IC-74153 (4:1 Multiplexer)

This IC chip contains two units of 4:1 MUXs with two common select inputs (S0, S1), but two separate active-low enable inputs. The block diagram of 74153 is shown in figure (2). Two select inputs S1 and S0 simultaneously control both sections of this MUX, but the two sections can be enabled or disabled by two independent Enable inputs, EN1 and EN2.

If S1=1 and S0=1. For example, the data through the input lines and 1I3 and 2I3 will be passed to the output 1Y and 2Y respectively provided both the strobe inputs are at logic 0. The data at the other inputs are irrelevant at this time. Now, if both the strobe inputs are at logic 1, then the data through the input lines are irrelevant at that time.

The function table for any section of this chip is shown in Table (2).

#### Truth Table for IC-74153

The two outputs 1Y and 2Y can be described by the following equation.

The expanded equation for the two outputs 1Y and 2Y are,

### IC-7486 (EX-OR Gate)

IC-7486 is a Quad 2-input EX-OR gate with 14-pin IC. It is widely used in the arithmetic section of a computer. These gates are widely used in digital design and therefore, are available in IC form Ex-OR has two inputs and an output. Output is 1 (High) only when the inputs are unequal and output is zero (LOW) when the inputs are the same. If they act as an equality detector. The pin diagram of the IC-7486 is Shown in figure (5).

### IC-7408 (AND Gate)

IC-7408 is a logic gate IC. It consists of four two-input AND gates. The AND gate performs a logical AND operation. Logic gates come in form of ICs. All four AND gates are independent. Each gate has three-pin two inputs and one output. The pin diagram of the IC-7408 is shown in figure (4).

So, thus we can say that the output of AND gate is HIGH only when both the inputs are in a HIGH state only. And in other cases, the output will be LOW.

### IC-7404 (NOT Gate)

The IC-7404 is a logic gate IC. It consists of six NOT gates. We know that the NOT gate is also called an inverter because it does complement any inputs. When applying a zero or LOW signal to the input, it gives a 1 or HIGH signal as in the output and vice versa. The pin diagram of the IC-7404 is shown in figure (3).

## PCB Design

For removing messy wiring and give a clean look, I designed a PCB prototype for this project. It is also helpful for troubleshooting that runs great without any errors. To design this PCB board, I used EasyEDA as it is too easy to use. For ordering PCB for this, I prefer PCBWay.

Gerber file for 2-Bit Multiplier Circuit Gerber.

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## Working Principle of 2-Bit Multiplier Circuit

Suppose you have two binary digits A1, A0, and B1, B0, here’s that multiplication would take place as:

In the above calculation, A1A0 is the multiplicand. B1B0 is the multiplier. The first product obtained from multiplying B0 with the multiplicand is called partial product 1. And the second product obtained from multiplying B1 with the multiplicand is known as the partial product 2.

But we do not derive any direct formulation for two 2-bit binary number multipliers from two multiplexers i.e., 4:1 MUX. So, here is the only way to derive it is just to make a detailed comparison from the Truth Table (5) given below.

#### Truth Table for multiplication, multiplier, multiplicand, and the product bits of (2×2) bit multiplication

The working of this project is very simple. You just need to know the concept of binary multiplication.

Here let the two 2-bit numbers be A = A1*A0 and B = B1*B0 and the product bits after multiplication are P3, P2, P1, and P0. Table (5) shows the multiplier B= B1*B0 and the multiplicand A= A1*A0 and the product bit P= P3, P2, P1, P0.

To produce the four product bits P0, P1, P2, and P3 we need four 4:1 MUX i.e., two IC-74153. The select inputs S1 and S0 of all the 4:1 MUX are common and are connected to A1 and A0 respectively. Since A1 and A0 are in a perfect sequence of (00, 01, 10, 11) and thus it gives a case to make the circuit easily.

Thus A1 and A0 act as select lines here. Now, for the remaining two bits (B1, B0) of input, we have to complex the inputs and outputs from Table (5).

For, A1A0 = 00[P0=0, P1=0, P2=0, P3=0]
01[P0=B0, P1=B1, P2=0, P3=0]
10[P0=0, P1=B0, P2=B1, P3=0]
11[P0=B0, P1=B1⊕B0, P2=B10, P3=B1B0]

So, to implement in circuit with MUX we should use XOR, AND and NOT GATE.

### Calculations for Current Limiting Resistance

We are using Green LEDs. The standard forward voltage across Green LED = 2.0V and the forward current is about = 20 mA. We are using 5V as supply voltage.

The current limiting resistor, RS = (5-2)/(2×10-3) = 150Ω.

So, the necessary value of the current limiting resistor is 150Ω and we are using a 220Ω practical value.

## Precautions & Discussions for 2-bit Multiplier Circuit

• Various resistance should be so chosen in the conduction state current through the LEDs. So that it does not exceed the maximum rated current. So carefully chose the safety resistance.
• The experiment has been done by using (+ve) level logic where a high voltage i.e., equal to (+VCC) 5V is taken as ‘1’ and a low voltage i.e., equal to ground 0V is taken as 0.
• LEDs with proper current limiting resistance can be used for easy, quick, and visual identification of 0 as OFF and 1 as ON state.
• While connecting the 5V DC supply to the IC, special care should be taken. Connection to any wrong pin can cause damage to the IC.
• For the multiplication circuit connect the S1 and S0 pin for both the IC-74153 carefully, if interchanged then the output will be disturbed.