p7 - Chapter 4 The Building Blocks Binary Numbers Boolean Logic and Gates INVITATION TO Computer Science Objectives After studying this chapter students

p7 - Chapter 4 The Building Blocks Binary Numbers Boolean...

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INVITATION TO Computer Science Chapter 4 The Building Blocks: Binary Numbers, Boolean Logic, and Gates
Objectives After studying this chapter, students will be able to: Translate between base-ten and base-two numbers, and represent negative numbers using both sign- magnitude and two’s complement representations Explain how floating-point numbers, character, sounds, and images are represented inside the computer Build truth tables for Boolean expressions and determine when they are true or false Describe the relationship between Boolean logic and computer hardware/circuits Invitation to Computer Science, 6th Edition 2
Objectives (continued) After studying this chapter, students will be able to: Construct circuits using the sum-of-products circuit design algorithm, and analyze simple circuits to determine their truth tables Explain how the compare-for-equality (CE) circuit works and its construction from one-bit CE circuits, and do the same for the adder circuit and its one-bit adder parts Describe the purpose and workings of multiplexor and decoder control circuits Invitation to Computer Science, 6th Edition 3
Introduction This chapter is about how computers work Problem: Execute Algorithms on Hardware => need value representation, hardware for logic & arithmetic, program execution All computing devices are built on the ideas in this chapter Laptops, desktops, Servers, supercomputers Game systems, cell phones, MP3 players Calculators, singing get-well cards Embedded systems, in toys, cars, microwaves, etc. Invitation to Computer Science, 6th Edition 4
The Binary Numbering System How can an electronic (or magnetic) machine represent information? Key requirements: clear, unambiguous, reliable External representation is human-oriented base-10 numbers keyboard characters Internal representation is computer-oriented base-2 numbers base-2 codes for characters “bistable” systems are reliable – transistor off/on Invitation to Computer Science, 6th Edition 5
Invitation to Computer Science, 6th Edition 6
The Binary Numbering System (continued) The binary numbering system is a base-2 positional numbering system Base ten: Uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Each place corresponds to a power of 10 1,943 = 1 * 10 3 + 9 * 10 2 + 4 * 10 1 + 3 * 10 0 Base two: Uses 2 digits: 0, 1 Each place corresponds to a power of 2 1101 = 1 * 2 3 + 1 * 2 2 + 0 * 2 1 + 1 * 2 0 = 13 Invitation to Computer Science, 6th Edition 7
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The Binary Numbering System (continued) Converting from binary to decimal Add up powers of two where a 1 appears in the binary number Converting from decimal to binary Repeatedly divide by two and record the remainder Example, convert 9: 9/2 = 4 remainder 1, binary number = 1 4/2 = 2 remainder 0, binary number = 01 2/2 = 1 remainder 0, binary number = 001 1/2 = 0 remainder 1, binary number = 1001 Invitation to Computer Science, 6th Edition 9
The Binary Numbering System (continued)

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