COMPSCI 210 Semester 1 - 2015 Tutorial 1. Binary to Decimal Conversion.
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Transcript of COMPSCI 210 Semester 1 - 2015 Tutorial 1. Binary to Decimal Conversion.
COMPSCI 210
Semester 1 - 2015
Tutorial 1
Binary to Decimal Conversion
2.10 Convert the following 2's complement binary numbers to decimal numbers.
a) 1010b) 01011010c) 11111110d) 0011100111010011
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)
2.10. d --- Solution • 0011100111010011
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)
= 8192 + 4096 + 2048 + 256+ 128 + 64 + 16 + 2 + 1
=14803
Decimal to Binary Conversion
2.11 convert these decimal numbers to 8 bit 2’s complement binary numbers.
a) 102b) 64c) 33d) -125e) 127
2.11.a --- Solution
• 102128 64 32 16 8 4 2 1
0 1 1 0 0 1 1 0
102
51 0
25 1
12 16 0
3 0
1 1
0 1
2.11.d --- Solution • -125
Two’s complement:
10000010 (flipping the digits above)+ 1 (adding “1”) 10000011
128 64 32 16 8 4 2 1
0 1 1 1 1 1 0 1
Decimal fractions to Binary
• (0.3125)10 = (?)2 0.3125 * 2 = 0.6250.625 * 2 = 1.250.25 * 2 = 0.50.5 * 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
2.39 Write IEEE floating point representation of the following decimal
numbers?a) 3.75b) -55.359375c) 3.1415927d) 64,000
2.39.b --- Solution
• -(55.359375)10 = -(110111.010111)2
• Normalizing the number -1.10111010111 . 25
• 1 10000100 10111010111000000000000
– The sign bit is 1, reflecting the fact that the number is a negative number
– The exponent: 5 = 132 – 127 =>10000100
2.39.d --- Solution
• (64,000)10 = (1111101000000000)2
• Normalizing the number 1111101000000000 = 1.111101000000000 . 2 15
• 0 10001110 11110100000000000000000– The sign bit is 0, reflecting the fact that the
number is a positive number – The exponent is 15 = 142 – 127
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