your monthly living expenses are $1500 on an income of $1,650 per month. your goal is to have an emergency fund of 4 times your
1 answer:
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Answer:
(a) 01 + 1011
Convert the two numbers into their 4-bit representation.
=> 01 = 0001
=> 1011
Addition of the two numbers (in their 2's complement form) gives the following:
0 0 0 1 ------------------> + 1 (in decimal)
<u>1 0 1 1 </u> ------------------> - 5 (in decimal)
<u>1 1 0 0 </u> -------------------> - 4 (in decimal)
Explanation for (a)
<em>01 or 0001</em>
Since the most significant bit is 0 (leftmost bit), it shows that it is a positive number. Therefore, it can be directly converted to its decimal representation as follows:
0001 = 0 x + 0 x
+ 0 x
+ 1 x
= 1
0001 is + 1 in decimal.
<em>1011</em>
Its most significant bit(MSB) is 1 showing that it is negative.
Flipping all its bits and adding 1 to the result, will convert it to it's positive counterpart.
i.e 1011 => 0100 + 1 = 0101.
Converting the result (0101) to decimal gives
0101 = 0 x + 1 x
+ 0 x
+ 1 x
= 5
1011 is -5 in decimal
<em>01 + 1011 or 0001+ 1011 = 1100</em>
The result (1100), of the addition of the two numbers, is a negative number as the MSB is 1.
Convert it to it's positive counterpart.
i.e 1100 => 0011 + 1 = 0100.
Converting the result (0100) to decimal gives
0100 = 0 x + 1 x
+ 0 x
+ 0 x
= 4
Therefore, the result, 1100 is -4 in decimal.
===================================================
(b) 11 + 01010101
Convert the two numbers into their 8-bit representation since one of them is in 8-bit.
PS: Taking 11, its MSB is 1 showing that it is a negative number. Also, it's 8-bit representation will mean pre-padding it with ones(1s) rather than zeros as follows. In other words, pre-padding a 2's complement number is done using its sign bit.
=> 11 = 11111111
=> 01010101
Addition of the two numbers (in their 2's complement form) gives the following:
1 1 1 1 1 1 1 1 ------------------> - 1 (in decimal)
<u> 0 1 0 1 0 1 0 1 </u> ------------------> + 85 (in decimal)
<u>1 0 1 0 1 0 1 0 0</u> -------------------> + 84 (in decimal)
Discard the carry-out bit (1) making the result 01010100
Explanation for (b)
<em>11 or 11111111</em>
Its MSB is 1 showing that it is negative.
Convert it to it's positive counterpart.
11111111 => 00000000 + 1 = 00000001
Converting the result (00000001) to decimal gives 1
11 or 11111111 is - 1 in decimal.
<em>01010101</em>
Its MSB is 0 showing that it is also positive. Now, convert to decimal
01010101 = 85
01010101 is + 85 in decimal.
<em>11111111 + 01010101 = 01010100</em>
The result (01010100), is also positive as the MSB is 0. Now, convert to decimal.
01010100 = 84
Therefore the result (01010100) is + 84 in decimal.
===================================================
(c) 0101 + 110
Convert the two numbers into their 4-bit representations.
=> 0101 = 0101
=> 110 = 1110
Addition of the two numbers (in their 2's complement form) gives the following:
0 1 0 1 ------------------> + 5 (in decimal)
<u> 1 1 1 0 </u> -----------------> - 2 (in decimal)
<u> 1 0 0 1 1 </u> -------------------> + 3 (in decimal)
Dicard the carry-out bit (leftmost bit) to get 0011 as result.
Explanation for (c)
<em>0101</em>
Since the MSB is 0 (leftmost bit), it shows that it is a positive number. Now, convert to decimal.
0101 = 5
0101 is +5 in decimal.
<em>110 or 1110</em>
Its MSB is 1 showing that it is negative.
Convert it to it's positive counterpart.
i.e 1110 => 0001 + 1 = 0010.
Converting the result (0010) to decimal gives
0010 = 2
1110 is -2 in decimal
<em>0101 + 110 = 0101+ 1110 = 0011</em>
The result (0011), is a positive number as the MSB is 0.
Converting the result (0011) to decimal gives
0011 = 3
Therefore, the result, 0011 is 3 in decimal.
===================================================
(d) 01 + 10
Convert the two numbers into their 4-bit representation.
=> 01 = 0001
=> 10 = 1110
Addition of the two numbers (in their 2's complement form) gives the following:
0 0 0 1 ------------------> + 1 (in decimal)
<u>1 1 1 0 </u> ------------------> - 2 (in decimal)
<u>1 1 1 1 </u> -------------------> - 1 (in decimal)
Explanation for (d)
<em>01 or 0001</em>
Since the MSB is 0 (leftmost bit), it shows that it is a positive number. Now convert to decimal.
0001 = 1
0001 is + 1 in decimal.
<em>1110</em>
Its MSB is 1 showing that it is negative.
Convert it to it's positive counterpart.
i.e 1110 => 0001 + 1 = 0010.
Converting the result (0010) to decimal gives
0010 = 2
1110 is -2 in decimal
<em>01 + 1011 or 0001+ 1110 = 1111</em>
The result (1111), is a negative number as the MSB is 1.
Convert it to it's positive counterpart.
i.e 1111 => 0000 + 1 = 0001.
Converting the result (0001) to decimal gives
0001 = 1
Therefore, the result, 1111 is -1 in decimal.
Answer:
Following are the correct python code to this question:
n1 = float(input('Input first number: '))#input first number
n2 = float(input('Input second number: '))#input second number
n3 = float(input('Input third number: '))#input third number
n4 = float(input('Input fourth number: '))#input fourth number
average = (n1+n2+n3+n4)/4 #calculate input number average
product = n1*n2*n3*n4 # calculate input number product
print('product: {:.0f} average: {:.0f}'.format(round(product),round(average))) #print product and average using round function
print('product: {:.3f} average: {:.3f}'.format(product,average)) #print product and average value
Output:
Please find the attachment.
Explanation:
The description of the above python code can be defined as follows:
- In the above python program four variable "n1, n2, n3, and n4" is defined, in which we take input from the user end, and in these user inputs we use the float method, that converts all the input value in to float value.
- In the next step, two variable average and product are defined, that calculate all input numbers product, average, and hold value in its variable.
- In the last line, the print method is used, which prints its variable value by using a round and format method.
