Transcript COMPSCI 210 Semester 2

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)
b)
c)
d)
1010
01011010
11111110
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)
b)
c)
d)
e)
102
64
33
-125
127
2.11.a --- Solution
• 102
128
0
64
1
32
1
16
0
8
0
4
1
102
51
0
25
1
12
1
6
0
3
0
1
1
0
1
2
1
1
0
2.11.d --- Solution
• -125
128
0
64
1
32
1
16
1
8
1
4
1
2
0
1
1
Two’s complement:
10000010 (flipping the digits above)
+
1 (adding “1”)
10000011
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
2.39 Write IEEE floating point
representation of the following decimal
numbers?
a)
b)
c)
d)
3.75
-55.359375
3.1415927
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