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Convert the denary number 132 into an 8 bit binary number - OCR - GCSE Computer Science - Question 5 - 2018 - Paper 1
Question 5
Convert the denary number 132 into an 8 bit binary number. Convert the binary number 10110101 to its hexadecimal equivalent. Show the effect of a binary shift righ... show full transcript
Worked Solution & Example Answer:Convert the denary number 132 into an 8 bit binary number - OCR - GCSE Computer Science - Question 5 - 2018 - Paper 1
Step 1
Convert the denary number 132 into an 8 bit binary number.
Answer
To convert the denary number 132 into an 8-bit binary number, we perform successive divisions by 2:
- 132 ÷ 2 = 66 remainder 0
- 66 ÷ 2 = 33 remainder 0
- 33 ÷ 2 = 16 remainder 1
- 16 ÷ 2 = 8 remainder 0
- 8 ÷ 2 = 4 remainder 0
- 4 ÷ 2 = 2 remainder 0
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top, 132 in binary is 10000100. To ensure it is 8 bits, we write it as: 10000100.
Step 2
Convert the binary number 10110101 to its hexadecimal equivalent.
Answer
To convert the binary number 10110101 into its hexadecimal equivalent, group the binary digits into nibbles:
- Split into two parts: 1011 0101.
- Convert each nibble to decimal:
- 1011 (binary) = 11 (decimal) = B (hexadecimal)
- 0101 (binary) = 5 (decimal) = 5 (hexadecimal)
Thus, the hexadecimal equivalent is B5.
Step 3
Show the effect of a binary shift right of two places on the binary number 00110100.
Answer
When we perform a binary shift right of two places on the binary number 00110100, the two rightmost digits are removed:
Original: 00110100 Shift right 2: 00001011.
This operation effectively divides the number by 4.
Step 4
Describe a shift that can be used to double the value of the binary number 00100100.
Answer
To double the value of the binary number 00100100, we can perform a left shift by one place. This moves all bits one position to the left, resulting in:
Original: 00100100 Left shift by 1: 01001000.
This operation effectively multiplies the number by 2.