SICS 154 DIGITAL COMPUTER FUNDAMENTAL

1
SICS 154 DIGITAL COMPUTER FUNDAMENTAL

• Prepared by Gabriel D. Kukuia

2
Reading List

• Digital Design by Morris Mano, published by
  Prentice Hall of India, 1995
• Digital Systems Principles Applications by
  Tocci.R. J, published by Prentice Hall of India,
  1995

3
Course Outline

• Digital Computers and Digital Systems
• Binary Systems
• Binary Numbers
• Number Base Conversion
• Octal and Hexadecimal Numbers
• Complements
• Binary Codes
• Binary Storage and Registers
• Binary Logic
• Integrated Circuits
• Boolean Algebra and Logic Gates
• Basic Definitions
• Axiomatic Definition of Boolean Algebra
• Basic theorems and Properties of Boolean
  Algebra
• Boolean Function
• Logic Operations
• Digital Logic Gates
• IC Digital Logic Families

4
Outline cont...

• Simplification of Boolean Functions
• The Map Method
• Two- and Three- Variable Maps
• Product of Sums Simplification
• NAND and NOR Implement
• The Tabulation Method
• Combinational Logic
• Introduction
• Design Procedure
• Adders
• Subtractors
• Analysis Procedure
• Multilevel NAND Circuits
• Multilevel NOR Circuits

5
Outline cont...

• Combinational Logic with MSI and LSI
• Introduction
• Binary Parallel Adder
• Decimal Adder
• Decoders
• Multiplexers
• Read Only Memory (ROM)
• Programmable Logic Array (PLA)
• Synchronous Sequential Logic
• Introduction
• Flip-Flops
• Design Procedure
• Design with State Equations
• Registers, Counters, And The Memory Unit
• Introduction
• Registers
• Shift Registers
• Counters
• The Memory Unit

6
Outline cont....

• Algorithmic State Machines (ASM)
• Introduction
• ASM Chart
• Design with Multiplexers
• PLA Control
• Asynchronous Sequential Logic
• Introduction
• Analysis Procedure
• Design Procedure
• Digital Integrated Circuits
• Introduction
• Transistor Transistor Logic (TTL)
• Metal-Oxide Semiconductor (MOS)
• Complementary MOS (CMOS)

7
Digital Computers Digital Systems

• Computers are used in
• Scientific calculations
• Commercial and business data processing
• Space guidance
• The educational field and many others
• Digital Computers follow a sequence of
  instructions, called a program, that operates on
  given data.
• The user can specify and change programs and/or
  data according to the specific need.

8
Types of Digital Computers

• General-purpose digital computer e.g. PC
• Specific-purpose digital computer e.g. telephone
  switching exchanges, digital voltmeter, frequency
  counters, calculating machines, teletype machine.

9
Characteristics of Digital Systems

• It is a manipulation of discrete elements of
  information. Such discrete elements may be
  electric impulses, the decimal digits, the
  letters of symbols. Early digital computers were
  used mostly for numerical computations.
• An analog computer performs a direct simulation
  of a physical system. The variables in the analog
  computer are represented by continuous signals
  usually electric voltages that vary with time.
  The term analog signal is sometimes substituted
  for continuous signal because analog computer
  has come to mean a computer that manipulates
  continuous variables.
• To simulate a physical process a digital
  computer, the quantities must be quantized. When
  the variables of the process are presented by
  real time continuous signals, the latter are
  quantized by an analog-to-digital device.

10
Block diagram of digital computer
11

• The memory unit stores programs as well as input,
  output, and intermediate data. The processor unit
  performs arithmetic.
• The processor unit performs arithmetic and other
  data processing task as specified by a program.
• The control unit supervises the flow of
  information between the various units. The
  control unit retrieves the instruction, one by
  one, from the program which is stored in memory.
  For each instruction, the control unit informs
  the processor to execute the operation specified
  by the instruction.
• Both program and data are stored in memory
  instructions, and the processor manipulates the
  data as specified by the program.

12

• The program and data prepared by the user are
  transferred into memory unit by means of an input
  device such as the punch-card reader or a
  teletypewriter.
• An output device, such as printer, receives the
  result of the computations and the printer
  results are presented to the user.
• The input and output devices are special digital
  systems driven by electromechanical parts and
  controlled by electronic digital circuits.
• A processor, when combine with the control unit,
  forms a component referred to as a central
  processor unit or CPU.
• The CPU enclosed in small integrated circuit
  package is called a microprocessor
• The CPU combined with memory and interface
  control to inform a small-size computer is called
  a microcomputer.

13
BINARY NUMBERS

• A decimal number such as 7392 represents a
  quantity equal to 7 thousands plus 3 hundreds,
  plus 9 tens, plus 2 units. The thousands,
  hundreds, etc., are powers of 10 implied by the
  position of the coefficients. To be more exact,
  7392 should be written as
• 7X 1033X1029X1012X100
• In general a5 a4 a3 a2 a1 a0 a-1 a-2 a-3
• aj coefficients are one of the ten digits
  (0,1,2,,9) and the subscript value j gives the
  place value and hence the power of 10 by which
  the coefficient must be multiplied.
• 105 a5 104a4 103a3 102a2 101a1 100a0
  10-1a-1 10-2a-2 10-3a-3
• The decimal number system is said to be of base,
  or radix, 10 because it uses ten digits and the
  coefficients are multiplied by powers of 10.
• The binary system is a different number system is
  a different number system. The coefficients of
  the binary numbers system have possible values 0
  and 1. Each coefficient aj is multiply by 2j

14

• Example
• 11010.11 is 26.75
• 1X24 1X230X221X210X201X211X2-2
• In general, a number expressed in base r system
  has coefficients multiplied by power of r
• anrn an-1rn-1 a2r2 a1r1 a0
  a-1r-1 a-2r-2 .. a-mr-m
• (4021.2)54X530X522X511X502X5-1

15

• For example, in the hexadecimal (base 16) number
  system, the first ten digits are borrowed from
  the decimal system. The letters A,B,C,D, E and F
  are used for 10,11,12,13,14,15 respectively.
• Example
• (B65F)16 11X1636X1625X16115X160
• Addition and Subtraction
• 101101 and 100111
• Multiplication
• 1011 and 101
• Number Base Conversions
• (1010.011)2 to base 10
• 1X230X221X211X2-21X2-3
• (10.375)10
• (630.4)86X823X814X8-1
• (408.5)10

16

• Convert decimal 41 to binary
• Integer quotient
  remainder coefficient
• 41/2 20 ½ a01
• 20/2 10 0 a10
• 10/2 5 0 a20
• 5/2 2 ½ a31
• 2/2 1 0 a40
• 1/2 0 ½ a51
• (41)10 ( a5 a4 a3 a2 a1 a0)2(101001)2

17
Alternative

• Integer remainder
• 41
• 20 1
• 10 0
• 5 0
• 2 1
• 1 0
• 0 1

18

• Convert 153 to octal ans (231)8
• Convert (0.6875)10 to binary
• Integer fraction
  coefficient
• 0.6875 X 2 1 0.3750
  a-11
• 0.3750 X 2 0 0.7500
  a-20
• 0.7500 X 2 1 0.5000
  a-31
• 0.5000 X 2 1
  0.0000 a-41
• (0.6875) (0. a-1 a-2 a-3 a-4)2(0.1011)2
• Convert (0.513)10 to octal
• 0.513 X 8 4.104
• 0.104 X 8 0.832
• 0.832 X 8 6.656
• 0.656 X 8 5.248
• 0.248 X 8 1.984
• 0.284 X 8 7.872
• (0.513)10 (0.406517..)8

19

• The conversion of decimal numbers with both
  integer and fraction parts is done by converting
  the integer and fraction separately and then
  combining the two answers together.
• (41.6875)10 (101001.1011)2
• (153.513)10 (231.406517)8
• EXX
• Convert the following
• (62.175)10 to base 2
• (185.165)10 to base 8

20

• The conversion from and to binary, octal, and
  hexadecimal plays an important part in digital
  computers. Since 238 and 2416, each octal digit
  corresponds to three binary digits and each
  hexadecimal digits corresponds to four binary
  digits.
• The conversion from binary to octal is easily
  accomplished by partitioning the binary number
  into groups of three digits each, starting from
  the binary point and proceeding to the left and
  to the right. The corresponding octal digit is
  then assigned to each group.
• Example
• (10 110 001 101 011 . 111 100 000 110 )2
• 2 6 1 5 3 7 4 0
  6
• (26153.7406)8
• (10 1100 0110 1011 . 1111 0010)2
• 2 C 6 B F 2
• (2C6B.F2)16
• (673.124)8 (110 111 011 . 001 010 100)2
• (306.D)16 (0011 0000 0110 . 1101)2

21

• Assignment 1
• 1. Write the first 20 decimal digits in base 3
• 2. Add and multiply the following numbers in the
  given base without converting to decimal.
• (i) (1230)4 and (23)4
• (ii) (135.4)6 and (43.2)6
• (iii) (367)8 and (715)8
• (iv) (296)12 and (57)12
• 3. Convert the decimal number 250.5 to base 3,
  base 4 base 7 and base 8, 16
• 4. Convert the following decimal to binary
  12.0625, 104, 673.23 and 198
• 5.Covert the following binary numbers to decimal
  10.10001, 101110.0101, 1110101.110, 1101101.111

22
Assignment 2

• 1. Convert the following numbers from the given
  base to the bases indicated
• 2. Decimal 225.225 to binary, octal and
  hexadecimal
• 3. Binary 11010111.110 to decimal, octal and
  hexadecimal
• 4. Octal 62377 to decimal binary and hexadecimal
• 5. Hexadecimal 2AC5.D to decimal, octal and
  binary
• 6. Convert the following numbers to decimal
• (i) (1001001.011)2
• (ii) (12121)3
• (iii) (1032.2)4
• (iv) (4310)5
• (v) (0.342)6
• (vi) (50)7
• (vii) (83)9
• (viii) (198)10