1. Course contents Chapter 1 - section 1.6 Chapter 2 - all sections Chapter 4 - 4.1 – 4.7, and 4.12 Chapter 5 - 5.1-5.3, 5.6-5.7 Chapter 6 - all sections Chapter 7 - all sections Chapter 8 - 8.1-8.9 1

2. 1.6 Binary numbers An electronic signal in logic circuits carries one digit of information. –Each digit is allowed to take on only two possible values, usually denoted as 0 and 1. –-> Information in logic circuits is represented as combinations of 0 and 1 digits. Q: How to represent numbers (E.g., positive integers) using only binary digits 0 and 1? 2

3. Decimal (base-10) number system A decimal integer is expressed by an n-tuple comprising n decimal digits D = d n-1 d n-2 ∙ ∙ ∙ d 1 d 0 which represents the value V(D) = d n-1 ×10 n-1 + d n-2 ×10 n-2 + ∙ ∙ ∙ + d 1 ×10 1 + d 0 ×10 0 This is referred to as the positional number representation. 3

4. Binary (base-2) number system Logic circuits use the binary system whose positional number representation is B = b n-1 b n-2 ∙ ∙ ∙ b 1 b 0 b n-1 is the most significant bit (MSB), b 0 is the least significant bit (LSB), Every bit b i can only have two values: 0 or 1. 4

5. Numbers in decimal and binary Decimal representation Binary representation 000000 010001 020010 030011 040100 050101 060110 070111 081000 Decimal representation Binary representation 091001 101010 111011 121100 131101 141110 151111 5

6. Conversion from binary to decimal Compute a weighted sum of every binary digit contained in the binary number B = b n-1 b n-2 ∙ ∙ ∙ b 1 b 0 V(B) = b n-1 ×2 n-1 + b n-2 ×2 n-2 + ∙ ∙ ∙ + b 1 ×2 1 + b 0 ×2 0 E.g., (1101) 2 = 1×2 3 + 1×2 2 + 0×2 1 +1×2 0 =(13) 10 6

7. Conversion from decimal to binary Perform the successive division by 2 until the quotient becomes 0. Remainder 857 / 2 = 4281LSB 428 / 2 = 2140 214 / 2 = 1070 107 / 2 = 531 53 / 2 = 261 26 / 2 = 130 13 / 2 = 61 6 / 2 = 30 3 / 2 = 11 1 / 2 = 01MSB 7

8. Chapter 2 Introduction to Logic Circuits

9. Outline 2.1 Variables and Functions 2.2 Inversion 2.3 Truth tables 2.4 Logic gates and networks 2.5 Boolean algebra 2.6 Synthesis using AND, OR and NOT gates 2.7 NAND and NOR logic networks 2.8 Design examples 9

10. Figure 2.1. A binary switch. x1=x0= (a) Two states of a switch S x (b) Symbol for a switch 2.1 Variables 10

11. Figure 2.2. A light controlled by a switch. (a) Simple connection to a battery S (b) Using a ground connection as the return path Battery Light Power supply S Light x x An application 11

12. Figure 2.3. Two basic functions. (a) The logical AND function (series connection) S Power supply S S Power supplyS (b) The logical OR function (parallel connection) Light x1x1 x2x2 x1x1 x2x2 Functions 12

13. S Power supplyS Light S X1X1 X2X2 X3X3 L(x 1, x 2, x 3 ) = (x 1 + x 2 ) x 3 A series-parallel connection 13

14. Figure 2.5. An inverting circuit. S Light Power supply R x 2.2 Inversion (complement, not) 14