1. Chapter 1: Digital Computers and Information Illustration at beginning of each Chapter Base 10 Binary Base 2 Octal Base 8 Hex bas 16 08 1000 10 8 15 1111 17 F BCD Binary Coded Decimal 4 bit code represents number 0-9 Base 10 BCD 00000 10001 91001 -Addition -Subtraction Parity Bit (checks for transmission errors Checks if total number of bits is even or odd Number even parity 100000101000001 101010011010100 Summary Page

2. Digital Computers Chapter 1: Logic Design deals with the basic concepts and tools used to design digital hardware consisting of logic circuits. Computer Design deals with the additional concepts and tools used to design computers and other complex digital hardware. Computers and digital hardware in general are referred to as digital systems. Characteristics of a digital system is the manipulation of discrete elements of information. Any set that is restricted to a finite number of elements contains discrete information. Examples of discrete sets are the 10 decimal digits, the 26 letters of the alphabet etc. Discrete elements of information are represented in a digital system by physical quantities called signals. Electrical signals such as voltages and currents are most common. Transistors dominate the circuitry that implements these signals. Signals in most present day electronic digitals systems ase just two discrete values and are therefore said to be binary. A Bipolar Transistor is a 3 terminal semiconductor sevice in which a small current at one terminal can control a much larger current flowing between the 2 nd and 3 rd terminal. Transistors can function both as amplifiers ans switches. +5V R2 1K Hi Lo +5V R1 1K LED S1 LED Lo Off Hi On And Gate +5V A 10K B 4.7K Out A B Out +5V Orange Boxes include information not in your text

3. Digital Computers Chapter 1: We typically represent two discrete values by ranges of voltages values called HIGH and LOW. The HIGH output voltage value ranges between 4.0 and 5.5 Volts The LOW output voltages ranges between -0.5 and 5.5 voltages The HIGH input range allows 3.0-5.5 volts to be recognized The LOW input ranges allow -0.5 to 2.0 volts. The fact that the input ranges are longer than the output ranges allows the circuits to function correctly in spite of variation in their behavior and undesirable noise voltages that may be added or subtracted from their outputs. Parity Bits: Used to detect errors (if there is excessive noise or errors, how would you detect it?) An additional bit is sometimes added to a binary code to make the total number of 1’s in the resulting code word even or odd. Original message(7 bits) Modified with Even Parity (8 Total bits) 1000001 (two 1’s) 0 1000001 (total # bits is even no change) 1010100 (three 1’s) 1 1010100 (total # bits is odd, so add a 1 so total is even four 1’s) Output 0.0 1.0 2.0 3.0 4.0 5.0 LOW (L) or False (F) or 0 HIGH (H) or True (T) or 1 INPUT LOW HIGH

4. Digital Computers Chapter 1: Why is Binary used? Consider a system with 10 values. The voltages between 0 and 5.0 volts would be divided into 10 ranges. Each of length 0.5 volt. A circuit with have to provide an output with each of these ranges. An input circuit would have to determine which of these belonged to each of these 10 ranges. If we wanted to compensate for noise that each range would be 0.25 volts. And the boundaries would be less than 0.25 volts This would require costly and complex electronic circuits and still would be disturbed by small noise voltages. Instead binary circuits are used with significant variation in output and input ranges. The resulting transistor circuit is simple, easy to design and extremely reliable. Information Representation: A Binary Digit is referred to as a bit. Information is represented as groups of bits. By using various coding schemes groups of bits can represent discrete symbols. 0000 0001 0010 0011 0100 0101 0110 American Standard Code for Information Interchange (7-bit code) (pg 25 text)

5. Digital Computers Chapter 1: Codes Unicode: A 16 bit code for representing the symbols and ideographs for the worlds languages. Gray Code: A code having the property that only one bit at a time changes between codes during counting is a Gray Code. Binary Coded Decimal: (BCD) Most commonly used code to represent decimal digits: (binary combinations 1010-1111 not used) DecimalBCD 00000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001

6. Octal: (base 8) Use symbols 0,1,2,3,4,5,6,7 8 3 8 2 8 1 8 0 Hexadecimal: (base 16): Use symbols 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F 16 3 16 2 16 1 16 0 Decimal: (base 10) Use symbols 0,1,2,3,4,5,6,7,8,9 10 4 10 3 10 2 10 0 Base 10Base 2Base 8Base 16 10010 18 4 2 164 8 1 256 16 1 10 2 10 1 10 0 2 3 2 2 2 1 2 0 8 2 8 1 8 0 16 3 16 1 16 0 10 0 0 1 0 0 10 0 1 101 0 1 00 1 20 0 A Value Power Digital Computers Chapter 1: Number Systems Power 10 Arithmetic Operations: Example 1: Base 10Base 2 100 10 1 16 8 4 2 1 Carries 0 0 0 0 0 1 2 0 1 1 0 0 + 1 7 + 1 0 0 0 1 ------- ------------- 2 9 1 1 1 0 1 Example 2: Base 10Base 2 100 10 1 32 16 8 4 2 1 Carries 1 0 1 1 0 0 2 2 1 0 1 1 0 + 2 3 + 1 0 1 1 1 ------- ------------- 4 5 1 0 1 1 0 1

7. Digital Computers Chapter 1: Number Systems Power 10 Example 1: Base 10Base 2 100 10 1 16 8 4 2 1 Borrows 0 0 1 1 0 2 2 1 0 1 1 0 - 1 9 - 1 0 0 1 1 ------- ------------- 0 3 0 0 0 1 1 The Rules for subtraction are the same in decimal. A borrow here adds 2 (in the decimal system a borrow adds 10) Column 1 Explanation Column 1 0 - 1 Cant take 1 from 0 so we borrow from the next column becomes 10 - 1 ------ 1 Column 2 1 - 1 This would normally be 0 (1-1) But we needed to borrow due to the first column, so 11 borrow 1 = 10 10 ---- 1 Example: (Base 10) 1 13 15 245 -1 - 9 7 - 197 ---- ---- ---- ------- 4 8 48 Borrow 1 1 Column 3 0 - 1 But we needed to borrow due to the second column, so 10 borrow 1 = 1 1 ---- 0 Starting Problem Result

8. Digital Computers Chapter 1: Number Systems Two’s Complement: (used to subtract two numbers by adding) (Hardware simpler) Subtract a number by converting the subtrahend to a two complement form then adding. Take the boolean complement of each bit, including the sign bit. -That is set each 1 to 0 and each 0 to 1. Then add 1 +18 = 00010010 Reverse the digits 11101101 Then add 1+1 ------------- 11101110 = -18 Example: 25 00011001 -18 00010010 B Register 18=00010010 Complementer 11101110 adder B Register 25=00011001 2 s compliment 00011001 + 11101110 --------------- 7=100000111 Overflow ignored Example: 18 00010010 00010010 11111001 -25 00011001 2 s complement 11100111 + 11100111 reverse digits 00000110 -------------- +1 011111001 Final answer 00000111 =- 7 Have to reverse process Result positive