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cs1101_09A_lec13

# cs1101_09A_lec13 - 5 5 0110 6 6 6 0111 7 7 7 1000 10 8 8...

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CS1101 - Lec02 1 Number Systems Number system Any system of naming or representing numbe rs. Also called numeral system The base of any number system is determine d by the number of digits in the system The number systems most commonly use d in computing are: Binary - 2 digits 0, 1 Octal - 8 digits 0, 1, 2, 3, 4, 5, 6, 7 Decimal - 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Hexadecimal - 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

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CS1101 - Lec02 2 Decimal: base-10 number syste m Hundreds Tens Ones Tenths Hundredths 102 101 100 10-1 10-2 3 7 5 . 1 5 3*102 = 3*100 = 300. 7*101 = 7*10 = 70. 5*100 = 5*1 = 5. 1*10-1 = 1*.1 = 0.1 5*10-2 = 5*.01 = + 0.05 375.15 Formula: ∑DIGIT * BASE POSITION #
CS1101 - Lec02 3 Binary: base-2 number system Formula: ∑DIGIT * 2 POSI TION # 24 23 22 21 20 2-1 2-2 1 1 1 0 1. 0 1 16 + 8 + 4 + 0 + 1 + 0 + 0.25 = 29.25 Octal and Hexadecimal Octal - base 8 number syst em Hexadecimal - base 16 nu mber system E.g., (for example) 2610 = 110102 = 328 = 1A16 Binar y Octal Decimal Hexa- decimal 0000 0 0 0 0001 1 1 1 0010 2 2 2 0011 3 3 3 0100 4 4 4 0101 5 5 5 0110 6 6 6 0111 7

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Unformatted text preview: 5 5 0110 6 6 6 0111 7 7 7 1000 10 8 8 1001 11 9 9 1010 12 10 A 1011 13 11 B 1100 14 12 C 1101 15 13 D 1110 16 14 E CS1101 - Lec02 4 Bit & Byte • Computers operate on binary numbers – Bit (Shortening for “ B inary dig IT ”) • The smallest unit of information • Can have one of two values : 1 or • Representing numbers, text characters, images , sounds, instructions and others – Byte : a collection of 8 bits 1 1 1 1 Least Significant Bit Most Significant Bit CS1101 - Lec02 5 Combining Bit Patterns • Using a single bit, with two discrete states, gives only two options (ON or OFF). • Combining more bits gives us more option s – 1 bit, 2 unique patterns: 0 or 1 – 2 bits, 4 unique patterns: 00, 01, 10 or 11 – 4 bits, 16 unique patterns: 0000, 0001, 0010, 0010, …1111 – 8 bits, 256 unique patterns: 00000000, 00000 Q: n bits will give you how many unique bit patterns?...
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