Chapter 7 Logic Circuits

1. Chapter 7Logic Circuits • State the advantages of digital technology compared to analog technology. • 2. Understand the terminology of digital circuits. • 3. Convert numbers between decimal, binary, and other forms.

2. 5. Understand the binary arithmetic operations used in computers and other digital systems. 6. Interconnect logic gates of various types to implement a given logic function. 7. Use Karnaugh maps to minimize the number of gates needed to implement a logic function.

6. Advantages of the Digital Approach Provided that the noise amplitude is not too large, the logic values represented by a digital signal can still be determined after noise is added. With modern IC technology, it is possible to manufacture exceedingly complex digital circuits economically.

7. Definitions Positive versus Negative Logic Digital Words In parallel transmission, an n-bit word is transferred on n wires, one wire for each bit, plus a common or ground wire. In serial transmission, the successive bits of the word are transferred one after the other with a single pair of wires.

8. Binary Numbers

15. Gray Code

17. Complement Arithmetic The one’s complement of a binary number is obtained by replacing 1s by 0s, and vice versa. 01001101 10110010 (one’s complement)

18. The two’s complement of a binary number is obtained by adding 1 to the one’s complement, neglecting the carry (if any) out of the most significant bit. Complements are useful for representing negative numbers and performing subtraction in computers.

21. Subtraction Using Two’s-Complement Arithmetic

22. Overflow and Underflow In performing arithmetic using two’s-complement arithmetic, we must be aware of the possibility of overflow in which the result exceeds the maximum value that can be represented by the word length in use.

32. Boolean algebra expressions can be implemented by interconnection of AND gates, OR gates, and inverters.

37. De Morgan’s Laws If the variables in a logic expression are replaced by their inverses, the AND operation is replaced by OR, the OR operation is replaced by AND, and the entire expression is inverted, the resulting logic expression yields the same values as before the changes.

39. NAND, NOR, and XOR Gates

42. Sum-of-Products Implementation Product terms that include all of the input variables (or their inverses) are called minterms. In a sum-of-products expression, we form a product of all the input variables (or their inverses) for each row of the truth table for which the result is logic 1. The output is the sum of these products.

45. Product-of-Sums Implementation Sum terms that include all of the input variables (or their inverses) are called maxterms. In a product-of-sums expression, we form a sum of all the input variables (or their inverses) for each row of the truth table for which the result is logic 0. The output is the product of these sums.

49. Karnaugh Maps