1. COMPSCI 210 Semester 1 - 2015 Tutorial 1

2. Binary to Decimal Conversion

3. 2.10 Convert the following 2's complement binary numbers to decimal numbers.
1010

4. 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)

5. 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

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
128 64 32 16 8 4 2 1
102 51 25 1 12 6 3

9. 2.11.d --- Solution
Two’s complement: (flipping the digits above) (adding “1”)
128 64 32 16 8 4 2 1

10. 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

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

12. 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 =>

13. 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

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