2. Chapter 2: Binary Values and Number Systems Chapter 2 Binary Values and Number Systems Page 14 Information may be reduced to its fundamental state by means of binary numbers (e.g., on/off, true/false, yes/no, high/low, positive/negative).Information may be reduced to its fundamental state by means of binary numbers (e.g., on/off, true/false, yes/no, high/low, positive/negative). “Bits” (binary digits) are used to accomplish this. Normally, we consider a binary value of 1 to represent a “high” state, while a binary value of 0 represents a “low” state.“Bits” (binary digits) are used to accomplish this. Normally, we consider a binary value of 1 to represent a “high” state, while a binary value of 0 represents a “low” state. In machines, these values are represented electronically by high and low voltages, and magnetically by positive and negative polarities.In machines, these values are represented electronically by high and low voltages, and magnetically by positive and negative polarities.

3. Binary Numerical Expressions Chapter 2 Binary Values and Number Systems Page 15 Binary expressions with multiple digits may be viewed in the same way that multi-digit decimal numbers are viewed, except in base 2 instead of base 10.Binary expressions with multiple digits may be viewed in the same way that multi-digit decimal numbers are viewed, except in base 2 instead of base 10. For example, just as the decimal number 275 is viewed as 5 ones, 7 tens, and 2 hundreds combined, the binary number 01010110 can be viewed in right-to-left fashion as...For example, just as the decimal number 275 is viewed as 5 ones, 7 tens, and 2 hundreds combined, the binary number 01010110 can be viewed in right-to-left fashion as... 01010110 0 ones0 ones 1 two1 two 1 four1 four 0 eights0 eights 1 sixteen1 sixteen 0 thirty-twos0 thirty-twos 1 sixty-four1 sixty-four 0 one hundred twenty-eights0 one hundred twenty-eights So, 01010110 is equivalent to the decimal number 2 + 4 + 16 + 64 = 86 01010110 01010110

4. Hexadecimal (Base-16) Notation Chapter 2 Binary Values and Number Systems Page 16 As a shorthand way of writing lengthy binary codes, computer scientists often use hexadecimal notation.As a shorthand way of writing lengthy binary codes, computer scientists often use hexadecimal notation. For example, the binary expression 1011001011101000 may be written in hexadecimal notation as B2E8. The two expressions mean the same thing, but they are in different notations. Binary Code Hexadecimal Notation 00000 00011 00102 00113 01004 01015 01106 01117 Binary Code Hexadecimal Notation 10008 10019 1010A 1011B 1100C 1101D 1110E 1111F