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CS101 Assignment 01 Fall 2020 Solution / Discussion

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CS101 Assignment 1 solution fall 2020 || CS 101

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CS101 Assignment No. 1 | Introduction to Computing | Hussain Sajid | Urdu / Hindi

Question No 1
Here we will show you step-by-step how to convert the decimal number 4789 to binary. Binary to Decimal

Answer :

First, note that decimal numbers use 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and binary numbers use only 2 digits (0 and 1).
As we explain the steps to converting 4789 to binary, it is important to know the name of the parts of a division problem. In a problem like A divided by B equals C, A is the Dividend, B is the Divisor and C is the Quotient.
The Quotient has two parts. The Whole part and the Fractional part. The Fractional part is also known as the Remainder.


Step 1) Divide 4789 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.



Step 2) Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.

Step 3) Repeat Step 2 above until the Whole part is 0.

Step 4) Write down the Remainders in reverse order to get the answer to 4789 as a binary.

Here we will show our work so you can follow along:

4789 / 2 = 2394 with 1 remainder
2394 / 2 = 1197 with 0 remainder
1197 / 2 = 598 with 1 remainder
598 / 2 = 299 with 0 remainder
299 / 2 = 149 with 1 remainder
149 / 2 = 74 with 1 remainder
74 / 2 = 37 with 0 remainder
37 / 2 = 18 with 1 remainder
18 / 2 = 9 with 0 remainder
9 / 2 = 4 with 1 remainder
4 / 2 = 2 with 0 remainder
2 / 2 = 1 with 0 remainder
1 / 2 = 0 with 1 remainder

Then, when we put the remainders together in reverse order, we get the answer. The decimal number 4789 converted to binary is therefore:

1001010110101

So what we did on the page was to Convert A10 to B2, where A is the decimal number 4789 and B is the binary number 1001010110101. Which means that you can display decimal number 4789 to binary in mathematical terms as follows:

478910 = 10010101101012

Binary To Decimal 

Here we will tell you what 1001010110101 binary is converted to decimal and then show you how we converted it. 1001010110101 binary converted to decimal is as follows:

1001010110101 = 4789

Here is how to convert 1001010110101 binary to decimal:

Step 1) Note that there are 13 digits in 1001010110101. That means there are 13 positions - the first position is the digit furthest to the right.

Step 2) Multiply the number in the first position by 20 (=1), the second position by 21 (=2), the third position by 22 (=4) and so on. (See Table 1 for longer list.) Here is the math for the 13 digits in 1001010110101:

1 x 1 = 1
0 x 2 = 0
1 x 4 = 4
0 x 8 = 0
1 x 16 = 16
1 x 32 = 32
0 x 64 = 0
1 x 128 = 128
0 x 256 = 0
1 x 512 = 512
0 x 1024 = 0
0 x 2048 = 0
1 x 4096 = 4096

Step 3) Finally, add up the answers from Step 2 to get the answer to 1001010110101 binary converted to decimal:

1 + 0 + 4 + 0 + 16 + 32 + 0 + 128 + 0 + 512 + 0 + 0 + 4096 = 4789

Once again, the answer is as follows:

1001010110101 = 4789

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