1. 1 Adders & Subtractors Adders –An adder is a combinational logic circuit that performs the addition of 2 binary numbers (A & B) to generate the sum (S) and an overflow indicator (O).

2. 2 Adders & Subtractors

3. 3 Subtractors A subtractor is a combinational logic circuit that performs the subtraction of 2 binary numbers (A & B) to generate the difference (D) and an underflow indicator (U).

4. 4 Half-Adder A combinational logic circuit that performs the addition of two binary digits (A & B) to generate the sum (S) and the carry (C). Design –Inputs: A & B –Outputs: C & S –Truth Table ABCS 0000 0101 1001 1110

5. 5 Half-Adder Boolean Expressions Circuit Diagram

6. 6 Full-Adder A combinational logic circuit that performs the addition of 2 binary digits (A & B) and a carry-in (CIN) from a lower significant digit to generate the sum (S) and the carry-out (COUT) to a higher significant digit. Design –Inputs: A, B, & CIN –Outputs: S & COUT

7. 7 Full-Adder Truth Table C IN ABC OUT S 00000 00101 01001 01110 10001 10110 11010 11111

8. 8 Full-Adder Boolean Expressions

9. 9 Full-Adder Circuit Diagram

10. 10 Code Conversion Different systems normally use different binary codes depending on the need of the system. It is sometimes necessary for use the output of one system as input to another system. Code conversion is necessary to make two systems using different binary codes compatible.

11. 11 Code Conversion Example The output of a measuring device that uses gray code is to be shown on a 7-segment display that uses BCD.  Gray Code-to-BCD Conversion

12. 12 Code Conversion Example ABCDWXYZ 00000000 00010001 00100011 00110010 01000111 01010110 01100100 01110101 Gray Code Values B C D First 8 inputs TRUTH TABLE

13. 13 Code Conversion Example 1000×××× 1001×××× 1010×××× 1011×××× 11001000 11011001 1110×××× 1111×××× ABCDWXYZ Gray Code Values B C D Last 8 inputs

14. 14 Code Conversion Example Boolean Expressions

15. 15 Code Conversion Example