## 4 Bit Adder Circuit:

Let us assume that the four bits in the 4-bit number A are A_{1},A_{2},A_{3} and A_{4} respectively. Thus the four bits of another number B are B_{1}, B_{2}, B_{3} and B_{4} . Since, Adder means addition, the sum of two four-bit numbers is calculated as-

If you notice in this case, it will be seen that the first digit is Carry Out (C_{0} ) [in this case C_{1} ], the second digit is Carry In (C_{i} ) [in this case it is C_{1}]. Similarly, the carry out of the second digit is (C_{0}) [in this case C_{2} ] followed by the carry out of the third digit [in this case it is C_{2}]. In this way the complete yoga is completed. The logic circuit that can be drawn by adding four bits from this is shown.

Looking at the logic circuit of 4 bit numbers, it can be seen that two bits have been added to each of the above 4 blocks and any block that carries out (eg C) acts as a carry in to the next block. All the outputs of this circuit ie C_{4},S_{4},S_{3},S_{2} and S_{1} are the sum of A and B.

## 4 Bit Subtractor Circuit:

Similar to Adder, let us assume that the four bits of the 4-bit number A are A_{1},A_{2},A_{3}, and A_{4}, and the four bits of the other 4-bit number E are E_{1}, E_{2}, E_{3}, and E_{4},.Since subtractor means subtraction, the subtraction of two four-bit numbers is calculated.

If you notice here, it will be seen that Borrow Out (B_{0}) of the first digit [in this case B_{1}] is Borrow In (B_{i}) of the second digit [in this case B_{1}]. Similarly, the second digit is Borrow out (B_{0} ) [in this case B_{2} ] and then the third digit is Borrow in (B_{i} ) [in this case also B_{2} ]. In this way the complete subtraction is done. From this the four bit subtraction logic circuit can be drawn.

Looking at the 4-bit logic circuit, it can be seen that two bits are subtracted in each of the four blocks and the Borrow Out of any block (eg B_{1}) acts as the Borrow In of the next block. All the outputs of this circuit i.e. B_{4}, D_{4}, D_{3}, D_{2} and D_{1} are the subtraction of A and E

## Frequently Asked Question (FAQs):

- 4 Bit Adder Circuit.
- 4 Bit Subtractor Circuit.