Question

Program 5: Decimal to Binary

In Computer Science we often work with different number systems to represent data. The most commonly used number system (which we refer to as "decimal") is a "base 10" number system, which means that we use the values 0-9 to represent all numbers.

The binary number system is a "base 2" number system, which means that we use the values 0 and 1 to represent all numbers. We refer to each value in a binary number as a "bit" (i.e. the number 0101 consists of 4 bits). Here are some numbers represented in both base 10 and base 2:

Decimal	Binary
0	0
1	1
2	10
3	11
10	1010
25	11001
65	1000001
127	1111111
128	10000000

This is the algorithm for converting a decimal number into a binary number:

• Attempt to divide the number by 2.
• If there is a remainder you should record the bit 1.
• If there is no remainder, you should record the bit 0.
• Divide the number by 2 and throw away the remainder.
• If the number is positive, repeat the process.
• If the number is 0, you should end the process.

Note that each successive bit you compute is for the next highest place (the next highest power of 2) -- so it will be inserted at the front (or the left-end) of the binary number.

For example, consider the following decimal number:

decimal = 5

Here is how the algorithm works on this number:

    5 ÷ 2 = 2 remainder 1               Record this bit:    1
    5 // 2 = 2
    2 ÷ 2 = 1 remainder 0               Record this bit:   01
    2 // 2 = 1
    1 ÷ 2 = 0 remainder 1               Record this bit:  101
    1 // 2 = 0 (algorithm stops)

For this problem, write a program that prompts the user for an integer greater than or equal to zero. If the user supplies a value less than 0 you should re-prompt them. Then convert the number to binary, printing out each step in the process as you go.

Note: Your binary value can't be recorded as an integer. Since you are building the number up bit-by-bit, you will probably need to keep track of 0's that are in higher place values than the the highest 1 bit, in other words, leading zeros. Integers do not support leading 0's (i.e. 0001 will be reduced to 1). Therefore, for this program you should use a String to hold your bits (i.e. "0001" is allowed). You will need to figure out a way how to add bits to your String (hint: concatenation)

Here are a few sample runnings of your program:

Enter a number greater than or equal to 0: -5
Invalid, try again
Enter a number greater than or equal to 0: -9
Invalid, try again
Enter a number greater than or equal to 0: 9
9 % 2 = 1 ---> 1
9 // 2 = 4
4 % 2 = 0 ---> 01
4 // 2 = 2
2 % 2 = 0 ---> 001
2 // 2 = 1
1 % 2 = 1 ---> 1001
1 // 2 = 0

9 in binary is 1001

Enter a number greater than or equal to 0: 86
86 % 2 = 0 ---> 0
86 // 2 = 43
43 % 2 = 1 ---> 10
43 // 2 = 21
21 % 2 = 1 ---> 110
21 // 2 = 10
10 % 2 = 0 ---> 0110
10 // 2 = 5
5 % 2 = 1 ---> 10110
5 // 2 = 2
2 % 2 = 0 ---> 010110
2 // 2 = 1
1 % 2 = 1 ---> 1010110
1 // 2 = 0

86 in binary is 1010110

Enter a number greater than or equal to 0: 255
255 % 2 = 1 ---> 1
255 // 2 = 127
127 % 2 = 1 ---> 11
127 // 2 = 63
63 % 2 = 1 ---> 111
63 // 2 = 31
31 % 2 = 1 ---> 1111
31 // 2 = 15
15 % 2 = 1 ---> 11111
15 // 2 = 7
7 % 2 = 1 ---> 111111
7 // 2 = 3
3 % 2 = 1 ---> 1111111
3 // 2 = 1
1 % 2 = 1 ---> 11111111
1 // 2 = 0

255 in binary is 11111111

Enter a number greater than or equal to 0: 256
256 % 2 = 0 ---> 0
256 // 2 = 128
128 % 2 = 0 ---> 00
128 // 2 = 64
64 % 2 = 0 ---> 000
64 // 2 = 32
32 % 2 = 0 ---> 0000
32 // 2 = 16
16 % 2 = 0 ---> 00000
16 // 2 = 8
8 % 2 = 0 ---> 000000
8 // 2 = 4
4 % 2 = 0 ---> 0000000
4 // 2 = 2
2 % 2 = 0 ---> 00000000
2 // 2 = 1
1 % 2 = 1 ---> 100000000
1 // 2 = 0

256 in binary is 100000000

This program should be named as follows: LastNameFirstName_assign4_problem5.py (for example, "KappCraig_assign4_problem5.py")

Answer 1

Program

# loop to get the positive number
while True:
    number=int(input("Enter a number greater than or equal to 0: "))
    # if number is positive, exit loop
    if number>0:
        break
    # else print message and continue loop
    print("Invalid, try again")

binary = '' # string for bianry
n = number # n is number
# loop to calculate binary
while n>0:
    # find the quotient by dividing n by 2
    quotient=n//2
    # find the remainder by modulus n by 2
    remainder=n%2
    # append remainder to the left of binary string
    binary = str(remainder) + binary
    # print quotient and remainder
    print(n,"% 2 =",remainder,"--->",binary)
    print(n,"// 2 =",quotient)
    # assign quotient to n
    n = quotient
# print binary representation
print("\n",number,"in binary is",binary)

Program screeshot for indentation reference

Sample outpte 1

Sample output 2

Sample output 3

Sample output 4