Question

Question: There are times when we want to add a collection of numbers together. Suppose you wanted to add four 4-bit numbers (A, B, E, F) using 1-bit full adders. Let’s ignore carry lookahead for now. You would likely connect the 1-bit adders in the organization at the top of Figure B.14.1. Below the traditional organization is a novel organization of full adders. Try adding four numbers using both organizations to convince yourself that you get the same answer.

Short answer

Answer

Adding four numbers using both organizations gives the same value.

Step-by-step solution

Consider any four 4-bit numbers A, B, C, and D

Suppose the four 4-bit numbers are:

A=1100

B=1011

C=1000

D=1110

The values of a3, a2, a1, a0 are 1, 1, 0, 0 respectively.

The values of b3, b2, b1, b0 are 1, 0, 1, 1 respectively.

The values of e3, e2, e1, e0 are 1, 0, 0, 0 respectively.

The values of f3, f2, f1, f0 are 1, 1, 1, 0 respectively.

Truth table for performing addition operation on traditional organization

The truth table for performing addition operations in a traditional organization is:

INPUTS		OUTUTS
A	B	SUM	CARRY
0	0	0	0
0	1	1	0
1	0	1	0
1	1	0	1

Addition of four numbers using traditional organization 

The following diagram shows the addition operation performed on the four 4-bit numbers A, B, C, and D.

The sum of the four numbers is 101101.

Truth table for performing addition operation on novel organization

The truth table for performing addition operation on a novel organization is:

INPUTS			OUTPUTS
A	B	Carry	Carry Out	SUM
0	0	0	0	0
0	0	1	0	1
0	1	0	0	1
0	1	1	1	0
1	0	0	0	1
1	0	1	1	0
1	1	0	1	0
1	1	1	1	1

Addition of four numbers using novel organization

The following diagram shows the addition operation performed on the four 4-bit numbers A, B, C, and D.