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5 (a) Convert the denary value 178 into an 8-bit binary number - OCR - GCSE Computer Science - Question 5 - 2021 - Paper 1
Question 5
5 (a) Convert the denary value 178 into an 8-bit binary number. (b) Computers make use of electronic switches called transistors. Describe how transistors can be us... show full transcript
Worked Solution & Example Answer:5 (a) Convert the denary value 178 into an 8-bit binary number - OCR - GCSE Computer Science - Question 5 - 2021 - Paper 1
Step 1
Convert the denary value 178 into an 8-bit binary number.
Answer
To convert 178 to binary, we can repeatedly divide by 2 and record the remainders. Starting with 178:
- 178 ÷ 2 = 89 remainder 0
- 89 ÷ 2 = 44 remainder 1
- 44 ÷ 2 = 22 remainder 0
- 22 ÷ 2 = 11 remainder 0
- 11 ÷ 2 = 5 remainder 1
- 5 ÷ 2 = 2 remainder 1
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
Now, reading the remainders from bottom to top, we get 10110010. Since it is an 8-bit number, we have:
Answer: 10110010
Step 2
Describe how transistors can be used to store a value in binary.
Answer
Transistors are fundamental components in computers that act as switches.
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ON and OFF States: A transistor can be in either an 'ON' (conducting) state or an 'OFF' (non-conducting) state. This binary representation is analogous to binary digits, where 'ON' can represent 1 and 'OFF' can represent 0.
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Data Storage: By organizing transistors in specific configurations, computers can use them to create memory cells. Each cell can hold one bit, enabling the storage of binary values.
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Logical Operations: Transistors enable logical operations. By combining multiple transistors, complex logical functions can be implemented, further enhancing data storage capabilities.
In summary, transistors are essential for storing binary values through their ability to represent the two states, contributing significantly to the functioning of memory in computers.
Step 3
Convert the binary value 11000111 into hexadecimal.
Answer
To convert the binary number 11000111 to hexadecimal, we can split it into groups of four bits from the right:
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Grouping: 1100 0111
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Converting each group to hexadecimal:
- 1100 is C
- 0111 is 7
Hence, the hexadecimal representation is:
Answer: C7
Step 4
Tick one box to identify whether Azmi is correct. Justify your answer.
Answer
Azmi's statement is Incorrect. Hexadecimal does not use less storage space than binary; it is simply a more compact representation of binary data. Each hexadecimal digit represents four binary digits, making it easier for humans to read large binary numbers, but it does not reduce the amount of memory required to store the information. Therefore, the storage requirement remains the same, regardless of representation.
Step 5
Draw one line from each shift on the left to its correct outcome on the right.
Answer
- Right shift of 2 places on 10101000 → 00101010, divides by 4 with a loss of precision.
- Left shift of 1 place on 00110100 → 01011000, multiplies by 2.
- Right shift of 2 places on 11110001 → 00111100, divides by 4 with a loss of precision.
- Left shift of 3 places on 00001111 → 1111000, multiplies by 8.
Step 6
Add the following 8 bit binary integers, giving your answer in binary.
Answer
To add the binary numbers:
00111010
- 10010110
We can perform binary addition:
- Start from the rightmost bit.
- 0 + 0 = 0
- 1 + 1 = 0 (carry 1)
- 1 + 1 + 1 (carry) = 1 (carry 1)
- Continue until all bits are added, including carry.
The result of the addition is:
Answer: 11010000