CS-1104 Spring-2021 - Homework 4
Arjun Dua
26 March 2021
Positive Integers:
- Smallest: 00000001 (1) - Largest: 01111111 (127)
Negative Integers: - Largest: 11111111(-1) - Smallest: 10000000 (-128)
Answer 1
As we can see above the range of numbers that can be stored is from -128 to 127.
Answer 2
Using the following algorithm (in Python), we get the results
def toBinary(x):
if x < 0:
x = 256+x
if x != 0:
remainder = x % 2
x = (x - remainder)/2
print (int(remainder))
toBinary(x)
print(toBinary(int(input("Enter x ="))))
1. 127 = 01111111
1
2. 126 = 01111110
3. 1 = 00000001
4. 0 = 00000000
5. -1 = 11111111
6. -2 = 11111110
7. -127 = 10000001
8. -128 = 10000000
Answer 3
Generalizing the bit-range formula we used to find the range of 8 − bit storage to get the formula for an n − bit
storage, we get
xn−bit ∈ [−(2n−1 ), 2n−1 − 1]
Therefore,
• Range of 16 − bit computer is, from −32768 to 32767
• Range of 32 − bit computer is, from −2147483648 to 2147483647
• Range of 64 − bit computer is, from −9223372036854775808 to 9223372036854775807
Answer 4
Finding the binary of 49, using the the code block given above in answer 2, we get
4910 = 001000112
Switching 1’s and 0’s and then adding 1, we get
2’s complement of 49 = 11001111
Thus to find 55 + (−49), we do the following addition
2
00110111
+
11001111
00000110
Answer 5
Since only the first two digits are 1’s we just have to perform the following addition(one left shift), we get
00100110
+
001001100
01110010
In decimal form, this is a multiplication between 38 and 3 which gives us 114, which matches the binary answer.
3