An arithmetic circuit in computer organization (CO) is a combinational circuit that performs arithmetic operations such as addition, subtraction, multiplication, and division on binary numbers. These circuits are widely used in digital systems such as microprocessors, calculators, and digital signal processing units.
Adders and subtractors are the basic building blocks of arithmetic circuits. An adder circuit takes two binary numbers as input and produces their sum as output. A subtractor circuit takes two binary numbers as input and produces their difference as output. Multiplication and division are more complex operations and require more complex circuits, such as multipliers and dividers.
Half – Adder:
A half-adder is a combinational circuit that performs binary addition of two bits, typically referred to as input A and input B, and produces two outputs: the sum (denoted as S) and the carry (denoted as C). The half-adder can only handle a single bit carry-in.
The truth table for a half-adder is as follows:
| Input A | Input B | Sum | Carry |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
As can be seen from the truth table, the sum output (S) is obtained by taking the exclusive-OR (XOR) of input bits A and B, while the carry output (C) is obtained by taking the logical AND of input bits A and B.
Full-adder:
A full-adder is a combinational circuit that performs binary addition of three bits: two single-bit inputs, typically referred to as A and B, and a carry-in bit, typically referred to as C_in. The full-adder produces two outputs: the sum (denoted as S) and the carry (denoted as C_out).
The truth table for a full-adder is as follows:
| A | B | C_in | S | C_out |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
As can be seen from the truth table, the sum output (S) is obtained by taking the exclusive-OR (XOR) of input bits A, B, and C_in, while the carry output (C_out) is obtained by taking the logical OR of the AND of input bits A and B, the AND of input bits B and C_in, and the AND of input bits A and C_in.
Half-Subtractor:
A half-subtractor is a combinational circuit that performs binary subtraction of two bits, typically referred to as input A and input B, and produces two outputs: the difference (denoted as D) and the borrow (denoted as B). The half-subtractor can only handle a single bit borrow-in.
The truth table for a half-subtractor is as follows:
| Input A | Input B | Difference | Borrow |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
As can be seen from the truth table, the difference output (D) is obtained by taking the exclusive-OR (XOR) of input bits A and B, while the borrow output (B) is obtained by taking the logical NOT of input bit A AND input bit B.
Full-Subtractor-
A full-subtractor is a combinational circuit that performs binary subtraction of three bits: two single-bit inputs, typically referred to as A and B, and a borrow-in bit, typically referred to as B_in. The full-subtractor produces two outputs: the difference (denoted as D) and the borrow (denoted as B_out).
The truth table for a full-subtractor is as follows:
| A | B | B_in | D | B_out |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
As can be seen from the truth table, the difference output (D) is obtained by taking the exclusive-OR (XOR) of input bits A, B, and B_in, while the borrow output (B_out) is obtained by taking the logical NOT of input bit A AND input bit B, OR the logical AND of input bit A and B_in, OR the logical AND of input bit B and B_in.
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