A 4-bit XS-3 parallel adder needs_____ 4-bit parallel adder IC 74

SOLUTION

Excess-3 Addition:

Step 1: We have to convert the numbers (which are to be added) into excess-3 by adding 0011 with each of the four-bit groups.

Step 2: Now the numbers are added using the basic laws of binary addition.

Step 3: Now, whichever of the four-bit groups have produced a carry, we have to add 0011 with them and subtract 0011 from the groups which have not produced a carry during the addition.

Step 4: The result which we have obtained after this operation is in Excess-3 form

Ex: (1)₁₀ + (4)₁₀ = (5)₁₀

XS – 3:    0100 + 0111 = 1011 = (11)₁₀

But we are supposed to get 1000, as XS-3 for (5)₁₀ is 1000.

So, we need to subtract 3 from the result

Ex: (6)₁₀ + (7)₁₀ = (13)₁₀

In XS-33: 1001 + 1010 = 10011

But we are supposed to get 0100 0110

So we need to add 011 to the result.

4-bit XS-3 Adder:

If C₄ = 1, then add three to the result (S₃ S₂ S₁ S₀)

If C₄ = 0, the subtract three (0011) from the result i.e. 2’s complement of three (1101) is added.

∴ Two 4-bit parallel adders are needed.