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A bit pattern is shown in Figure 1 - AQA - GCSE Computer Science - Question 1 - 2021 - Paper 1
Question 1
A bit pattern is shown in Figure 1. 01001110 1. Convert the bit pattern shown in Figure 1 into decimal. 2. Convert the bit pattern shown in Figure 1 into hexadeci... show full transcript
Worked Solution & Example Answer:A bit pattern is shown in Figure 1 - AQA - GCSE Computer Science - Question 1 - 2021 - Paper 1
Step 1
Convert the bit pattern shown in Figure 1 into decimal.
Answer
To convert the binary number 01001110 to decimal, we assign powers of 2 to each digit starting from the right:
0 * 2^7 + 1 * 2^6 + 0 * 2^5 + 0 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0
This simplifies to:
0 + 64 + 0 + 0 + 8 + 4 + 2 + 0 = 78.
Step 2
Convert the bit pattern shown in Figure 1 into hexadecimal.
Answer
To convert the binary number 01001110 to hexadecimal, we group the bits into sets of four from right to left:
0010 0111 0 -> 0010 0111 (we fill in leading zeroes)
Then we convert each group to hexadecimal:
0010= 20111= 7
Therefore, 01001110 in hexadecimal is 4E.
Step 3
Explain why the student's answer is incorrect.
Answer
The student's answer is incorrect because, while hexadecimal does use fewer digits than binary, both numbers will still occupy the same amount of memory space when stored. This is because the actual number itself, when converted to binary, will take the same bits regardless of the representation system used.
Step 4
Explain how a binary number can be multiplied by 8 by shifting bits.
Answer
A binary number can be multiplied by 8 by shifting its bits to the left by three positions. This is because shifting left by one position is equivalent to multiplying by 2. Therefore, to multiply by 8 (which is ), we shift by three positions. For example, the binary number 00000110 (which is 6 in decimal) when shifted left three times becomes 00110000, which equals 48 in decimal.
Step 5
Step 6
State two advantages of using Unicode to represent characters instead of ASCII.
Answer
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Wider Character Set: Unicode supports a far larger number of characters than ASCII, accommodating characters from multiple languages and scripts.
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Global Compatibility: Unicode provides a universal standard for text representation, which helps maintain consistent encoding across different platforms and applications, ensuring that text appears correctly worldwide.