ALU Design

ALU Design

1. Arithmetic Circuits

• We have already seen how parallel adder can be constructed using number of full adder circuits connected in cascade. Let us see the implementation of various functions of arithmetic unit using parallel adder. Table 2.8.1 shows these implementations.

• Looking at Table 2.8.1 we can realize that by selecting proper B and C_in inputs we can implement basic arithmetic operations. There are four possible B inputs: true, complement, all 1s and all 0s and two possible C_in inputs 0 and 1.

• Referring Table 2.8.2, we can write truth table for B input with respect to So and S1 signals as follows:

Note‒ B' indicates modified B input

K‒map simplification

• Using the logic diagram of modified B input we can draw the logic diagram of arithmetic circuit, as shown in Fig. 2.8.2. (See Fig. 2.8.2 on next page).

• We can also implement the arithmetic circuit using multiplexers. Refer Table 2.8.4, we have four options for the B input of the full adder. We have to select one of the four options according to select input S₁ and S₀. We can implement a circuit for such requirement using 4:1 multiplexer. Fig. 2.8.3 shows the arithmetic circuit using multiplexers. (Refer Fig. 2.8.3 on page 2‒79)

• By controlling the value of B input of full adder with the two select inputs S₁ and S₀ and making C_in equal to 0 to 1, it is possible to generate the eight arithmetic micro‒operations listed in Table 2.8.3.

Example: 1

Draw the block diagram for the hardware that implements the following statements:

i) x + yz : AR←AR + BR

 ii) x + xy + xz : AR←AR +1.

Solution:

i) Fig. 2.8.4 shows the hardware that implements statement

x+yz: AR← AR + BR and statement x + xy + xz: AR ← AR + 1.

2. Logic Circuits

• The design of logic circuit is comparatively simple than the design of arithmetic circuit. Fig. 2.8.5 shows the function table and the logic diagram for logic circuit.

Note: The logic diagram shown in Fig. 2.8.5 (b) is repeated n times for n‒bit logic circuit. Therefore, inputs A and B, and output Y are shown with subscript i, where i = 1, 2, ... n

Review Questions

1. Explain the 4‒bit arithmetic circuit using the multiplexer.

2. Explain the 4‒bit arithmetic circuit with its function table.

3. Explain the design of the logic circuit using the multiplexer.