1. 디지털 로직 및 CAD 실습 Fundamentals of Logic Design (6e) Charles H. Roth, Jr.
교 재
Fundamentals of Logic Design (6e)
Charles H. Roth, Jr.
점 수
중간•기말 시험: 70%
실험: 20%
출석: 10%
연 락 처
조우연 (특허청, ,
주의 사항
실험 : PSpice (OrCAD)
디자인한 프로젝트 회로 및 결과 프린트 출력 / 결과(진리표 작성)
Fundamentals of Logic Design Chap. 1

2. INTRODUCTION NUMBER SYSTEMS AND CONVERSION
CHAPTER 1
INTRODUCTION NUMBER SYSTEMS AND CONVERSION
This chapter in the book includes:
Objectives
Study Guide
1.1 Digital Systems and Switching Circuits
1.2 Number Systems and Conversion
1.3 Binary Arithmetic
1.4 Representation of Negative Numbers
1.5 Binary Codes
Problems
Fundamentals of Logic Design Chap. 1

3. Objectives Topics introduced in this chapter:
Difference between Analog and Digital System
Difference between Combinational and Sequential Circuits
Binary number and digital systems
Number systems and Conversion
Add, Subtract, Multiply, Divide Positive Binary Numbers
1’s Complement, 2’s Complement for Negative binary number
BCD code, code, excess-3 code
아날로그시스템과 디지털 시스템의 차이점
조합회로와 순서회로의 차이점
2진수와 디지털시스템
진법 변환(2진수, 4진수 8진수 10진수, 16진수)
2진수의 사칙연산
1의 보수, 2의 보수(음수의 표현)
BCD코드, 6311코드, 초과-3 코드, 가중치 코드 등
Fundamentals of Logic Design Chap. 1

4. 1.1 Digital Systems and Switching Circuits
computation, data processing, control, communication, measurement
Reliable, Integration
Analog – Continuous
- Natural Phenomena
(Pressure, Temperature, Speed…)
- Difficulty in realizing, processing using electronics
Digital – Discrete
- Binary Digit  Signal Processing as Bit unit
- Easy in realizing, processing using electronics
- High performance due to Integrated Circuit Technology
Fundamentals of Logic Design Chap. 1

5. Binary Digit? Binary Good things in Binary Number Two values(0, 1)
Each digit is called as a “bit”
Good things in Binary Number
Number representation with only two values (0,1)
Can be implemented with simple electronics devices
(ex: Voltage High(1), Low(0) ; Switch On (1) Off(0)…)
Fundamentals of Logic Design Chap. 1

6. Figure 1-1: Switching circuit
Combinational Circuit :
outputs depend on only present inputs, not on past inputs
Sequential Circuit:
outputs depend on both present inputs and past inputs
have “memory” elements
Figure 1-1: Switching circuit
Fundamentals of Logic Design Chap. 1

7. 1.2 Number Systems and Conversion
Decimal:
Binary:
Radix(Base):
Octal-Decimal:
Hexa-Decimal:
Fundamentals of Logic Design Chap. 1

8. 1.2 Number Systems and Conversion
Conversion of Decimal to Base-R
Fundamentals of Logic Design Chap. 1

9. 1.2 Number Systems and Conversion
Example: Decimal to Binary Conversion 53 2 26 13 6 3 1
rem. = 1 = a0
rem. = 0 = a1
rem. = 1 = a2
rem. = 0 = a3
rem. = 1 = a4
rem. = 1 = a5
Fundamentals of Logic Design Chap. 1

10. 1.2 Number Systems and Conversion
Conversion of a decimal fraction to Base-R
Example:
Fundamentals of Logic Design Chap. 1

11. 1.2 Number Systems and Conversion
Example: Convert 0.7 to binary
Process starts repeating here because .4 was previously
obtained
Fundamentals of Logic Design Chap. 1

12. 1.2 Number Systems and Conversion
Example: Convert to base-7 45 7 6
rem.6
rem.3
Conversion of Binary to Hexa
Fundamentals of Logic Design Chap. 1

13. 1.2 Number Systems and Conversion
Conversion of Binary to Octal, Hexa-decimal
( )2
= ( )8, octal
( )2
( )2
= ( )16, Hexadecimal
( )2
= ( )16, Hexadecimal
Fundamentals of Logic Design Chap. 1

14. 1.3 Binary Arithmetic Addition Example: and carry 1 to the next column
carries
Fundamentals of Logic Design Chap. 1

15. 1.3 Binary Arithmetic Subtraction Example:
and borrow 1 from the next column
Example:
(indicates
a borrow
From the
3rd column)
borrows
Fundamentals of Logic Design Chap. 1

16. 1.3 Binary Arithmetic Subtraction Example with Decimal column 2
note borrow from column 1
note borrow from column 2
Fundamentals of Logic Design Chap. 1

17. 1.3 Binary Arithmetic Multiplication Multiply: 13 x11(10) multiplicand
multiplier
first partial product
second partial product
sum of first two partial products
third partial product
sum after adding third partial product
fourth partial product
final product (sum after adding fourth partial prodoct)
Fundamentals of Logic Design Chap. 1

18. 1.3 Binary Arithmetic Division The quotient is 1101 with a remainder
of 10.
Fundamentals of Logic Design Chap. 1

19. 1.4 Representation of Negative Numbers– 1 1
Magnitude
MSB
(a) Unsigned number b b b b n – 1 n – 2 1
Magnitude
Sign
0 denotes +
MSB
1 denotes –
(b) Signed number
Fundamentals of Logic Design Chap. 1

20. 1.4 Representation of Negative Numbers
2’s complement of a positive integer N
Table 1-1: Signed Binary Integers (word length n = 4)
Fundamentals of Logic Design Chap. 1

21. 1.4 Representation of Negative Numbers
1’s complement of a positive integer N
Example:
== 2’s complement: 1’s complement + ‘1’
Fundamentals of Logic Design Chap. 1

22. 1.4 Representation of Negative Number
Addition of 2’s complement Numbers
(correct answer)
Case 1
Case 2
wrong answer because of overflow (+11 requires
5 bits including sign)
Case 3
(correct answer)
Case 4
correct answer when the carry from the sign bit
is ignored (this is not an overflow)
Fundamentals of Logic Design Chap. 1

23. 1.4 Representation of Negative Numbers
Addition of 2’s complement Numbers
Case 5
correct answer when the last carry is ignored
(this is not an overflow)
Case 6
wrong answer because of overflow
(-11 requires 5 bits including sign)
Fundamentals of Logic Design Chap. 1

24. 1.4 Representation of Negative Numbers
Addition of 1’s complement Numbers
Case 3
(correct answer)
Case 4
(end-around carry)
(correct answer, no overflow)
Case 5
(end-around carry)
(correct answer, no overflow)
Fundamentals of Logic Design Chap. 1

25. 1.4 Representation of Negative Numbers
Addition of 1’s complement Numbers
Case 6
(end-around carry)
(wrong answer because of overflow)
Fundamentals of Logic Design Chap. 1

26. 1.4 Representation of Negative Numbers
Addition of 1’s complement Numbers
(end-around carry)
Addition of 2’s complement Numbers
(discard last carry)
Fundamentals of Logic Design Chap. 1

27. 1.5 Binary Codes
Fundamentals of Logic Design Chap. 1

28. 1.5 Binary Codes 6-3-1-1 Code: ASCII Code
S t a r t
Fundamentals of Logic Design Chap. 1

29. Table 1-3 ASCII code (incomplete)
1.5 Binary Codes
Table 1-3 ASCII code (incomplete)
Fundamentals of Logic Design Chap. 1