Answer to Question #93229 in Programming & Computer Science for Tah

Question

How the carry bit act as an extension to the arithmetic and logic unit (ALU)? Explain briefly with examples?

Answer 1

An electronic circuit that adds up two binary numbers.

XOR consists another logic gates:

$$\iff$$

The top picture shows a half adder.

A is the first binary number. B is the second binary number. They are summed using XOR (upper logic gate). Carry is defined using AND (lower logic gate).

XOR (Sum Out) and AND (Carry Out)

A - 0, B - 0: Sum Out - 0 and Carry Out - 0;

A - 0, B - 1: Sum Out - 1 and Carry Out - 0;

A - 1, B - 0: Sum Out - 1 and Carry Out - 0;

A - 1, B - 1: Sum Out - 0 and Carry Out - 1.

We can denote the half adder in this way:

Then the full adder is denoted in this way:

So, Carry Out of the previous half adder is summed with the result of the following half adder.

We can denote the full adder in this way:

The binary adder consists of full adders (for example, 8-Bit Sum):

And we can denote it in this way:

16-bit adder consists two 8-Bit Adder etc.