Lec 01 - Microcomputer Architecture and Logic Design
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The document provides an overview of microcomputer architecture and logic design, focusing on number systems including decimal and binary representation, number-base conversions, and methods such as complements for arithmetic operations. It outlines the course structure, including references, mark allocation, and the content covered in classes, such as combinational and sequential logic. Additionally, it includes examples and explanations of concepts like 2's complement and radix complement used for digital computations.
Lec 01 - Microcomputer Architecture and Logic Design
- 1. To know Introduction Number Systems Microcomputer Architecture and Logic Design (CST161-3) Vajira Thambawita Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 2. To know Introduction Number Systems Table of contents 1 To know References Mark Allocation 2 Introduction Contents 3 Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 3. To know Introduction Number Systems References Mark Allocation Time Theory - Monday 8.00 - 10.00 Practical - Wednesday 1.00-2.00 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 4. To know Introduction Number Systems References Mark Allocation References Digital Design and Computer Architecture, David Money Harris and Sarah L. Harris Digital Design with an introduction to the Verilog HDL, M. Morris Mano and Michael D. Ciletti Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 5. To know Introduction Number Systems References Mark Allocation Mark Allocation Continuous Mark - 40% Practical Exam (After the mid break) - 20% Hardware Assignment (Group work 3 members per group) - 10% 2 x Pop Quizzes - 10% End Exam - 60% Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 6. To know Introduction Number Systems Contents Contents Combinational Logic, Combinational Circuit Design and Analysis, Binary Adder-Subtractor, Decoders, Encoders, Multiplexers Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 7. To know Introduction Number Systems Contents Contents Combinational Logic, Combinational Circuit Design and Analysis, Binary Adder-Subtractor, Decoders, Encoders, Multiplexers Sequential Logic, Latches, Flip-Flops, Sequential Circuit analysis and Design Procedure Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 8. To know Introduction Number Systems Contents Contents Combinational Logic, Combinational Circuit Design and Analysis, Binary Adder-Subtractor, Decoders, Encoders, Multiplexers Sequential Logic, Latches, Flip-Flops, Sequential Circuit analysis and Design Procedure Digital Circuit Design and Implementation, Organization and Implementation of Different Architectures, 8086 architecture, Instructions, memory organization, Buses, Interrupt, IO operations Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 9. To know Introduction Number Systems Contents Contents Combinational Logic, Combinational Circuit Design and Analysis, Binary Adder-Subtractor, Decoders, Encoders, Multiplexers Sequential Logic, Latches, Flip-Flops, Sequential Circuit analysis and Design Procedure Digital Circuit Design and Implementation, Organization and Implementation of Different Architectures, 8086 architecture, Instructions, memory organization, Buses, Interrupt, IO operations Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 10. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Decimal Number 7392 = 7 × 103 + 3 × 102 + 9 × 101 + 2 × 100 In general, a number with a decimal point is represented by a series of coefficients: a5a4a3a2a1a0.a−1a−2a−3 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 11. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Binary Numbers only two possible values: 0 and 1 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 12. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Binary Numbers only two possible values: 0 and 1 11010.11 ? Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 13. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Binary Numbers only two possible values: 0 and 1 11010.11 ? 11010.11 -? 1×24 +1×23 +0×22 +1×21 +0×20 +1×2−1 +1×2−2 = 26.75 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 14. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Binary Numbers only two possible values: 0 and 1 11010.11 ? 11010.11 -? 1×24 +1×23 +0×22 +1×21 +0×20 +1×2−1 +1×2−2 = 26.75 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 15. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Powers of two Figure: Powers of two Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 16. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Convert decimal 41 to binary Convert decimal 153 to octal Convert (0.6875)10 to binary Convert (0.513)10 to octal Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 17. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Number-base conversions Convert decimal 41 to binary Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 18. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Number-base conversions Convert decimal 153 to octal Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 19. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Number-base conversions Convert (0.6875)10 to binary Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 20. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Number-base conversions Convert (0.513)10 to octal Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 21. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Number-base conversions Octal and Hexadecimal Numbers Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 22. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems COMPLEMENTS OF NUMBERS Complements are used in digital computers to simplify the subtraction operation and for logical manipulation There are two types of complements for each base-r system: the radix complement (the r’s complement) the diminished radix complement (the (r-1)’s complement) Examples 2’s complement and 1’s complement for binary numbers the 10’s complement and 9’s complement for decimal numbers Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 23. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Diminished Radix Complement (r-1)’s complement Given a number N in base r having n digits, the (r -1)’s complement of N = (rn − 1) − N The 9’s complement of 546700 The 9’s complement of 012398 The 1’s complement of 1011000 The 1’s complement of 0101101 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 24. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Diminished Radix Complement The 9’s complement of 546700 is 999999-546700= 453299. The 9’s complement of 012398 is 999999 -012398=987601. The 1’s complement of 1011000 is 0100111. The 1’s complement of 0101101 is 1010010. Do you know? the 1’s complement of a binary number is formed by changing 1’s to 0’s and 0’s to 1’s Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 25. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement r’s complement The r’s complement of an ndigit number N in base r is defined as rn − N for N = 0 0 for N=0 Do you know? the r’s complement is obtained by adding 1 to the (r-1)’s complement Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 26. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 27. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 28. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 29. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is 753300 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 30. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is 753300 the 2’s complement of 1101100 is Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 31. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is 753300 the 2’s complement of 1101100 is 0010100 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 32. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is 753300 the 2’s complement of 1101100 is 0010100 the 2’s complement of 0110111 is Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 33. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is 753300 the 2’s complement of 1101100 is 0010100 the 2’s complement of 0110111 is 1001001 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 34. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Radix Complement Examples the 10’s complement of 012398 is 987602 the 10’s complement of 246700 is 753300 the 2’s complement of 1101100 is 0010100 the 2’s complement of 0110111 is 1001001 Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 35. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Subtraction with Complements The subtraction of two n-digit unsigned numbers M-N in base r can be done as follows: 1 Add the minuend M to the r’s complement of the subtrahend N. Mathematically, M + (rn − N) = M − N + rn. 2 If M ≥ N, the sum will produce an end carry rn, which can be discarded, what is left is the result (M-N). 3 If M < N, the sum does not produce an end carry and is equal to rn − (N − M), which is the r’s complement of (N-M). To obtain the answer in a familiar form, take the r’s complement of the sum and place a negative sign in front. Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 36. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems To Do Given the two binary numbers X=1110100 and Y=1000101, perform the subtraction X-Y and Y-X by using 2’s complements Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 37. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Range of N-bit numbers Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)
- 38. To know Introduction Number Systems Decimal Binary Numbers Number-base conversions Complements of numbers Diminished Radix Complement Radix Complement Subtraction with Complements Example Comparison of Number Systems Signed Binary Numbers Vajira Thambawita Microcomputer Architecture and Logic Design (CST161-3)