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**COMPSCI 210 Semester 1 - 2015 Tutorial 1**

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**Binary to Decimal Conversion**

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**2.10 Convert the following 2's complement binary numbers to decimal numbers.**

1010

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2.10. c --- Solution sign bit is 1, so this number is negative. Calculate the 2's complement (flipping the digits above) = -2 (Affix a minus sign in front)

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2.10. d --- Solution sign bit is 0, so this number is positive. =0*(2^14)+1*(2^13)+1*(2^12)+1*(2^11)+0*(2^10)+0*(2^9)+1*(2^8)+1*(2^7)+1*(2^6)+0*(2^5)+1*(2^4)+0*(2^3)+0*(2^2)+1*(2^1)+1*(2^0) =1*(2^13)+1*(2^12)+1*(2^11)+1*(2^8)+1*(2^7)+1*(2^6)+1*(2^4)+1*(2^1)+1*(2^0) = =14803

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**Decimal to Binary Conversion**

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**2.11 convert these decimal numbers to 8 bit 2’s complement binary numbers.**

102 64 33 -125 127

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2.11.a --- Solution 102 128 64 32 16 8 4 2 1 102 51 25 1 12 6 3

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2.11.d --- Solution Two’s complement: (flipping the digits above) (adding “1”) 128 64 32 16 8 4 2 1

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**Decimal fractions to Binary **

(0.3125)10 = (?)2 * 2 = 0.625 0.625 * 2 = 1.25 0.25 * 2 = 0.5 0.5 * 2 = 1.0 (0.3125)10 = (0.0101)2 (0.0101)2 = (0. 0*2-1+1*2-2+0*2-3+1*2-4) = ( )10 = (0.3125)10

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**2.39 Write IEEE floating point representation of the following decimal numbers?**

3.75 64,000

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2.39.b --- Solution -( )10 = -( )2 Normalizing the number The sign bit is 1, reflecting the fact that the number is a negative number The exponent: 5 = 132 – 127 =>

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2.39.d --- Solution (64,000)10 = ( )2 Normalizing the number = The sign bit is 0, reflecting the fact that the number is a positive number The exponent is 15 = 142 – 127

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ASCII Codes ASCII stands for American Standard Code For Information Interchange. Each key on the keyboard is identified by its unique ASCII code When you type a key on the keyboard, the corresponding eight-bit code is stored and made available to the computer Most keys are associated with more than one code, for example, h and H have two different codes

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©Brooks/Cole, 2003 Chapter 3 Number Representation.

©Brooks/Cole, 2003 Chapter 3 Number Representation.

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