Chapter02 - Chapter 2: Binary Values and Chapter Number...

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Unformatted text preview: Chapter 2: Binary Values and Chapter Number Systems • Information may be reduced to its fundamental state by means of binary Information numbers (e.g., on/off, true/false, yes/no, high/low, positive/negative). numbers • “Bits” (binary digits) are used to accomplish this. Normally, we Bits” consider a binary value of 1 to represent a “high” state, while a binary value of 0 represents a “low” state. value • In machines, these values are represented electronically by high and In low voltages, and magnetically by positive and negative polarities. low Chapter 2 Binary Values Binary and Number Systems Systems Page 1 Page Binary Numerical Expressions Binary • Binary expressions with multiple digits may be viewed in the same way Binary that multi-digit decimal numbers are viewed, except in base 2 instead of base 10. base • For example, just as the decimal number 275 is viewed as 5 ones, 7 For tens, and 2 hundreds combined, the binary number 01010110 can be viewed in right-to-left fashion as... viewed 01010110 01010110 01010110 01010110 01010110 01010110 01010110 0101011 1010110 • • • • • • • • 0 ones 1 two 1 four 0 eights 1 sixteen 0 thirty-twos 1 sixty-four 0 one hundred twentyeights So, 01010110 So, is equivalent to the decimal number 2 + 4 + 16 + 64 = 86 16 Chapter 2 Binary Values Binary and Number Systems Systems Page 2 Page Hexadecimal (Base-16) Notation Hexadecimal • As a shorthand way of writing lengthy binary codes, computer As scientists often use hexadecimal notation. hexadecimal Binary Hexadecimal Binary Hexadecimal Code Notation Code Notation 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 For example, the binary For expression 1011001011101000 may be written in hexadecimal notation as B2E8. as The two expressions The mean the same thing, mean but they are in different notations. notations Binary Hexadecimal Binary Hexadecimal Code Notation Code Notation 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F Chapter 2 Binary Values Binary and Number Systems Systems Page 3 Page ...
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