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COMPSCI 210 Semester 1 - 2014

COMPSCI 210 Semester 1 - 2014. Tutorial 1. Binary to Decimal Conversion. 2.10 Convert the following 2's complement binary numbers to decimal numbers. 1010 01011010 11111110 0011100111010011. 2.10. c --- Solution . 1 1111110 sign bit is 1 , so this number is negative.

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COMPSCI 210 Semester 1 - 2014

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  1. COMPSCI 210Semester 1 - 2014 Tutorial 1

  2. Binary to Decimal Conversion

  3. 2.10 Convert the following 2's complement binary numbers to decimal numbers. • 1010 • 01011010 • 11111110 • 0011100111010011

  4. 2.10. c --- Solution • 11111110 • sign bit is 1, so this number is negative. • Calculate the 2's complement.0000001 (flipping the digits above)+ 1 0000010= -2 (Affix a minus sign in front)

  5. 2.10. d --- Solution • 0011100111010011sign 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)= 8192 + 4096 + 2048 + 256+ 128 + 64 + 16 + 2 + 1=14803

  6. Decimal to Binary Conversion

  7. 2.11 convert these decimal numbers to 8 bit 2’s complement binary numbers. • 102 • 64 • 33 • -125 • 127

  8. 2.11.a --- Solution • 102

  9. 2.11.d --- Solution • -125Two’s complement: 10000010 (flipping the digits above)+ 1 (adding “1”) 10000011

  10. Decimal fractions to Binary • (0.3125)10 = (?)2 • 0.3125 * 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. 0 + 0.25 + 0 + 0.0625)10 = (0.3125)10

  11. 2.39 Write IEEE floating point representation of the following decimal numbers? • 3.75 • -55.359375 • 3.1415927 • 64,000

  12. 2.39.b --- Solution • -(55.359375)10 = -(110111.010111)2 • Normalizing the number -1.10111010111 . 25 • 11000010010111010111000000000000 • The sign bit is 1, reflecting the fact that the number is a negative number • The exponent: 5 = 132 – 127 =>10000100

  13. 2.39.d --- Solution • (64,000)10= (1111101000000000)2 • Normalizing the number 1111101000000000 = 1.111101000000000 . 2 15 • 01000111011110100000000000000000 • The sign bit is 0, reflecting the fact that the number is a positive number • The exponent is 15 = 142 – 127

  14. 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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