Chapter 1 Introduction to Computers
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Chapter 1 Introduction to Computers. Maran Illustrated Computers CIS 102. Hardware. Software. Getting Help. How Computers Work in General. Input devices. Process (CPU). Output. Storage device. Data representation in Bytes. Computer Memory.
Chapter 1 Introduction to Computers
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Chapter 1 Introduction to Computers Maran Illustrated Computers CIS 102
Computer Memory • Memory is comprised of a large collection of bi-state (off/on) electrical devices called bits (binary digits) • A single bit can assume the value 0 or 1. • A single bit is not sufficient to represent all data ; therefore, it is necessary to use a sequence of bits.
Computer Memory • How many bits are needed in a bit pattern to represent a symbol in a language? • A bit pattern of size 1 can represent two different pieces of information. For example, to represent pass / fail we could use 0 - Fail 1 - Pass
Binary system • The binary system is based on 2. • There are only two digits: 0 and 1 • We convert a number from binary to decimal by multiplying each binary digit by its corresponding power of 2. i.e. Multiply the bit at position n (n = 0, 1, 2, …) by
Figure 3-1 Decimal system
Figure 3-2 Binary system
Binary system Binary to Decimal Conversion Binary number
Figure 3-3 Binary to decimal conversion
Exercises • Convert the binary number 10011 to decimal. • Convert the binary number 1110101 to decimal.
Example 1 Convert the binary number 10011 to decimal. Solution Write out the bits and their weights. Multiply the bit by its corresponding weight and record the result. At t Write out the bits and their weights. Multiply the bit by its corresponding weight and record the result. At the end, add the results to get the decimal number. Binary 1 0 0 1 1Weights 16 8 4 2 1 ------------------------------------- 16 + 0 + 0 + 2 + 1
Exercises • Convert the decimal number 35 to binary. • Convert the decimal number 327 to binary.
Octal Digit------------ 0 1 2 3 Bit Pattern------------ 000 001 010 011 100 101 110 111 4 5 6 7 Base 8 (Octal ) Valid digits: 0, 1, 2, 3, 4, 5, 6, 7
Bit Pattern------------ 0000 0001 0010 0011 0100 0101 0110 0111 Hex Digit------------ 0 1 2 3 4 5 6 7 Bit Pattern------------ 1000 1001 1010 1011 1100 1101 1110 1111 Hex Digit------------ 8 9 A B C D E F Base 16 - Hexadecimal Valid digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Converting from base 2 to hexadecimal • To convert from base 2 to hexadecimal • Organize the stream of binary digits into groups of four. • Find the hexadecimal value for each group of 4 bits. 10010010111000011010 1001 0010 1110 0001 1010 9 2 E 1 A
Converting from hexadecimal to base 2 • To convert from hexadecimal (base 16) to base 2 Convert each digit to its 4-bit equivalent. 9 2 E 1 A 1001 0010 1110 0001 1010
Binary to hexadecimal and hexadecimal to binary transformation
Exercises • Show the hexadecimal equivalent of the bit pattern 1100 1110 0010. • Show the hexadecimal equivalent of the bit pattern 0011100010. • What is the bit pattern for 2675 base 16? • What is the bit pattern for B51E base 16?
Review number systems • Review base 10 • Review base 2 (binary) • Review base 16 (hexadecimal) • Convert from decimal to binary • Convert from binary to decimal • Convert between binary and Hexadecimal • See notes for links covering these topics
