Question

1. Create the following circuits in Logisim as you have seen the instructor do on the lectures. DO NOT use built-in MUX, ADDER or D-Latch for this.
   1. A 6-to-1 mux using basic gates (AND, OR)
   2. A four-bit full adder. Create a 1-bit adder first and then use it as a block to create a four-bit adder.
   3. A 1 bit gated D-Latch and then reuse it to as a block create a two-bit D-Latch.

Answer 1

Following circuits are designed using Logisim, Here we have not used the built-in MUX, ADDER or D-Latch

a) A 6-to-1 MUX using basic gates:

A 6-to-1 MUX will have six inputs and one output. This circuit will require 3 select inputs. Here S₂ S₁ S₀ are the three select inputs, and I₀ I₁, I₂, I₃, I₄, and I₅ are the six inputs of a 6-to-1 multiplexer. Depending on the value in the select input, one input will be selected and passed to the output.

The following logisim diagram shows a 6-to-1 MUX designed using basic logic gates.

The truth table of a 6:1 MUX that used for the deisgn is given below:

The output is the OR of multiple AND terms. Here the first AND term from the truth table is S₂'S₁'S₀'I₀

Similarly, we can find the other AND terms to obtain the circuit of 6:1 MUX.

Here, the select inputs are shown as 000 and the output is I₀ or the value of the I₀ input which is 0 here

When select input S₂S₁S₀=001 then the output is I₁ or the value of the I₁ input which is 1 here

When select input S₂S₁S₀=010 then the output is I₂ or the value of the I₂ input which is 0 here

When select input S₂S₁S₀=011 then the output is I₃ or the value of the I₃ input which is 1 here​​​​​​​

When select input S₂S₁S₀=100 then the output is I₄ or the value of the I₄ input which is 1 here​​​​​​​

When select input S₂S₁S₀=101 then the output is I₅ or the value of the I₅ input which is 0 here​​​​​​​

Here care must be taken not to give 110 and 111 as the select inputs, as these are invalid select inputs for a 6-to-1 MUX.

b) A four-bit full adder using four 1-bit adders

We will design a one-bit adder circuit that will add two one-bit numbers A and B and will output the sum and carry.

The truth table of a one-bit full adder is shown below:

This circuit designed using logisim using logic gates is shown below:

This 1-bit full adder will add two 1-bit numbers (A and B) and product the sum output bit and a carry output bit. Provision is made to add the input carry C also if any. If there is no input carry this C input bit will always be 0.

Now we can use the above one-bit adder as a block to create a four-bit adder. We have used the four blocks of one-bit full adder designed earlier to design this four-fit full adder in logisim as shown below:

Here two four-bit numbers A₃A₂A₁A₀ is added with B₃B₂B₁B₀ to obtain the output S₃S₂S₁S₀ along with a carry output Cout

Also, the addition of two four-bit numbers 1001 + 1101 is shown below in the logisim circuit, the input and output can be observed. The output is 0110 with an output carry of 1. This is illustrated in the following diagram:

c) A 1 bit gated D-Latch and then reuse it to as a block create a two-bit D-Latch

The 1-bit gated D-latch is shown below designed using logisim:

Here, the circuit is enabled or made active when we give logic 1 to the Enable input.

When D=0, Q=0 and

when D=1, Q=1

Now, we can reuse this to design a 2-bit gated D-latch in logisim as shown below:

Here, in the 2-bit gated latch, two input bits are D₀ D₁ and the outputs are Q₀ Q₁