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5 (a) Convert the hexadecimal number A3 to denary - OCR - GCSE Computer Science - Question 5 - 2019 - Paper 1

Question 5

5 (a) Convert the hexadecimal number A3 to denary. Show your working. (b) Convert the binary number 1011011 to denary. Show your working. (d) Add the following bin... show full transcript

Worked Solution & Example Answer:5 (a) Convert the hexadecimal number A3 to denary - OCR - GCSE Computer Science - Question 5 - 2019 - Paper 1

Step 1

Convert the hexadecimal number A3 to denary. Show your working.

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Answer

To convert the hexadecimal number A3 to denary, we first break it down by digit:

A in hexadecimal is equivalent to 10 in denary.
3 in hexadecimal is equivalent to 3 in denary.

We can express A3 in terms of its place values:

$ext{A3} = 10 \times 16^1 + 3 \times 16^0$

Now calculating this gives us:

$10 \times 16 + 3 \times 1 = 160 + 3 = 163$

Thus, the denary representation of hexadecimal A3 is 163.

Step 2

Convert the binary number 1011011 to denary. Show your working.

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Answer

To convert the binary number 1011011 to denary, we identify the positional values:

The binary number is written as:

$1 \times 2^6 + 0 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0$

Calculating each term results in:

$64 + 0 + 16 + 8 + 0 + 2 + 1 = 91$

Therefore, the denary representation of binary 1011011 is 91.

Step 3

Add the following binary numbers:

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Answer

To add the binary numbers 1010110 and 1000111:

    1010110
  + 1000111
  ----------
   10011001

To carry out the addition from right to left:

0 + 1 = 1
1 + 1 = 0 (carry over 1)
1 + 1 + 1 = 1 (carry 1)
0 + 0 + 1 = 1
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0 (carry over 1)
Finally, write down the carry 1 to the leftmost side.

Thus, the result of adding 1010110 and 1000111 is 10011001.

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Questions answered

5 (a) Convert the hexadecimal number A3 to denary - OCR - GCSE Computer Science - Question 5 - 2019 - Paper 1

Worked Solution & Example Answer:5 (a) Convert the hexadecimal number A3 to denary - OCR - GCSE Computer Science - Question 5 - 2019 - Paper 1

Convert the hexadecimal number A3 to denary. Show your working.

Convert the binary number 1011011 to denary. Show your working.

Add the following binary numbers:

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