The World’s Largest Online Community for Developers

';
How the logical XOR and NOT operations are available in the arithmetic operation of ALU? - LavOzs.Com
logical-operators xor digital-logic alu complement

**Problem**

For different combinations of selection bits and input carry, we can perform different arithmetic operations as found in this book *(Figure 1, given below)*. Similarly, for different combinations of selection bits, we can perform different logical operations *(Figure 2, given below)*. This book mentioned that two of the logical operations *(XOR and NOT)* already available *(So far I understand from this book and class lecture, they referred that these two operations are available in the arithmetic operations figure)*. But I did not find any similar operation in arithmetic operation figure.

Basically, I wanted to get the explanation of the highlighted line.

(Picture is from Digital Logic and Computer Design)

**What I think after going through class lectures and the referred book**

In the arithmetic operations figure, we find one decrement operation *(F=A-1)*. And in this operation, if we give input 1 *(A=1)*, we will get output 0 *(F=0)*. On the otherhand, if we set input 0 *(A=0)*, we will get nonzero value *(F=2^n - 1)* as an output. And this resembles a logical complement operation. So, maybe they referred this decrement operation as an available operation for NOT operation.

In case of X-OR operation, they maybe referred the arithmetic add *(basically OR)* operation *(F=A+B)*.

**So, What confuses me**

When we get input 0 for variable A, we get output *2^n-1* for the decrement function *(F=A-1)*. It *(2^n-1)* is not equal to 1 which we would get as an output for the logical complement operation. So, how the decrement function *(F=A-1)* can resemble the logical NOT operation ?

OR operation gives 1 as an output even when all inputs are 1, which is zero regarding X-OR operation. So, OR and X-OR operation are not similar. So, how OR operation can resemble the logical XOR operation?

**My Question**

How the logical XOR and NOT operations are available in the arithmetic operation? More explicitly, Which operations of arithmetic unit they (i.e. XOR and NOT) resemble and how?

** Figure 1: Arithmetic Operations**, Collected from Digital Logic and Computer Design

** Figure 2: Logical Operations**, Collected from Digital Logic and Computer Design

Related

How do you get the logical xor of two variables in Python?

Creating a “logical exclusive or” operator in Java

Logical XOR operator in C++?

Why is there no logical xor in JavaScript?

Simple logical operators in Bash

Exclusive logical sum (XOR)

How to concatenate 3 operation select bits in a 4-bit ALU design - VHDL

Are || and ! operators sufficient to make every possible logical expression?

For how many values of x will n + x = n XOR x when n and x are whole numbers and n>=x?

How do you get the logical xor of two variables in Python?

Creating a “logical exclusive or” operator in Java

Logical XOR operator in C++?

Why is there no logical xor in JavaScript?

Simple logical operators in Bash

Exclusive logical sum (XOR)

How to concatenate 3 operation select bits in a 4-bit ALU design - VHDL

Are || and ! operators sufficient to make every possible logical expression?

For how many values of x will n + x = n XOR x when n and x are whole numbers and n>=x?