2014F001/User talk:KatieMay/homework 4
From CDS 130
8.75/12: See comments in italic. Chris 19:02, 22 October 2014 (UTC)
1. Variables are programmer-designated names that can represent a specific value of data. Like other programming languages, MATLAB also has a set of rules for naming variables. If the rules are violated, the variables can not be treated as valid variables, causing programming errors.
Create four "invalid" variable names with different reasons, and state the reason why the variable names can not be used in MATLAB.
@Katie variable cannot start with @ sign
7Katie variable cannot start with a number
_K variable cannot start with underscore
K$ variable cannot include $ symbol
2. Without running Matlab, what output results from running the following Matlab code?
%% A matlab code to test arithmetic functions. a = 3; b = 4; c = a*b; a = a + 2 b = b + 2; a = mod (c, a); b = mod (c, b); a b
Your Answer:
a=2
b=0
3. Use Matlab to evaluate the following expressions.
- floor(7.6)
- ceil( − 3.4)
- round(5.5)
sqrt(2)*pi^3
ans =43.8495
pi/(sin(1.2)*cos(6.0))
ans =
3.5105
(.0000123+5.678*10^-4)*0.1234*10^-4
ans =
7.1584e-09
mod(3,4)
ans =
3
mod(4,3)
ans =
1
floor(7.6)
ans =
7
ceil(-3.4)
ans =
-3
round(5.5)
ans =
6
4. Anonymous function in Matlab
An anonymous function defined in matlab is a function that is not stored in a program file, but associated with a variable. Provide a matlab script in which a mathematical function f(x,y) is defined as
f(x,y) = cos(x^{3}) + sin(y^{3}) + e^{x+y}
Calculate the values of f(0.3,0.2), f(3,2), f(π, π / 2) using the defined anonymous function in Matlab.
f(0.3,0.2)
ans =
2.6564
f(3,2)
ans =
149.1104
f(pi, pi/ 2)
ans =
111.5651
5. Suppose that you have defined the function foo as follows
function y = foo(x) z = x + 2; y = x * z^2; end
what are the values from the following calls?
>> foo(2)=32
>> foo(foo(2))=36992
6. Write a Matlab function (m file) to evaluate the function logfunc(x) = log10(x^{2}), and (1) show your m-file for this function; (2) calculate logfunc(3.2) and logfunc(-5.0)
You have the wrong function. See solution below. -1 Chris
7. Sign-and-magnitude
Use the sign-and-magnitude method to represent the signed number (-101)_{10} in 8 bits.
1 1 0 0 1 0 1
See solution below. -1 Chris
The magnitude (101)_{10} can be represented by seven bits. The eighth bit will be used for the sign.
1 | 1 | 0 | 0 | 1 | 0 | 1 | |
2^{6} | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} | |
64 + | 32 + | 0 + | 0 + | 4 + | 0 + | 1 = | 101 |
The last bit will be 1 to denote the negative sign. Thus, the answer is (1110 0101)_{2}.
8. One's complement
Convert One's Complement numbers to base ten numbers.
- 10001010=117
- 01110110=-118
Answer:
- 10001010=117
- 01110110=-118
Opposite signs. -0.5 Chris
9. Two's Complement
Form the negative or positive equivalent of the following 8-bit Two's Complement numbers
- 00011001
- 10101010
Answer:
11100111
01010111
10. One's complement
For the computer architecture using two's complement to represent negative numbers, what is the minimum number of bits needed to represent (-255)_{10}.
9
11. Representing Negative Numbers
For an 8-bit group, work out the representation for − 87_{10} in
a) Sign & Magnitude
11010111
b) One's Complement
10101000
c) Two's Complement
10101001
d) Excess-127 00101000
12. Suppose signed integers are represented by 10 bits in a computer architecture. Show respectively the range of the integers (in base 10) in the following methods:
a) Sign & Magnitude
(-511 to 511)
b) One's Complement
(-1023 to 1023)c) Two's Complement (-1023 to 1023)
d) Excess-127-1150 to 1150
Your ranges for One's/Two's Complement and Excess-127 are wrong. Please review your ranges. -0.75 Chris