QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
1.1 Convert the binary 1101001 to:
a) Decimal (base 10)
b) Octal
c) Hexadecimal
1.2 Determine:
a) - 109 mod 13
b) The time a 24 -hour clock that reads 15:00 ten thousand hours prior
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Answer
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Step 1: Converting binary 1101001 to decimal (base 10)
1101001_{2} = 1 imes 2^{6} + 1 imes 2^{5} + 0 imes 2^{4} + 1 imes 2^{3} + 0 imes 2^{2} + 0 imes 2^{1} + 1 imes 2^{0}
To convert binary to decimal, we multiply each digit by its corresponding power of 2, starting from 0 at the right and increasing by 1 as we move to the left. So, for the binary number 1101001, we have:
Step 2: Calculate the decimal equivalent
1101001_{2} = 64 + 32 + 0 + 8 + 0 + 0 + 1 = 105
Now, let's calculate the decimal equivalent:
Final Answer
Step 3: Converting binary 1101001 to octal To convert binary to octal, we group the binary digits into sets of 3, starting from the right and adding leading zeros if necessary. Then, we convert each group to octal. For binary 1101001, we have: 1101001_{2} = (001) (101) (001) Now, convert each group to octal: (001)_{2} = 1_{8} (101)_{2} = 5_{8} (001)_{2} = 1_{8} Step 4: Combine the octal groups Combine the octal groups to get the 1101001_{2} = 151_{8} Step 5: Converting binary 1101001 to hexadecimal To convert binary to hexadecimal, we group the binary digits into sets of 4, starting from the right and adding leading zeros if necessary. Then, we convert each group to hexadecimal. For binary 1101001, we have: 1101001_{2} = (0001) (1001) Now, convert each group to hexadecimal: (0001)_{2} = 1_{16} (1001)_{2} = 9_{16} Step 6: Combine the hexadecimal groups 1101001_{2} = 19_{16} Step 7: Determine - 109 mod 13 To find the modulus of - 109 divided by 13, we perform the division and find the remainder. - 109 = - 8 imes 13 + 5 The remainder is 5. Step 8: Determine the time 10,000 hours prior to 15:00 on a 24 -hour clock To find the time 10,000 hours prior to 15:00, we subtract 10,000 from 15:00. Since 15:00 is 15 hours after midnight, we can represent the time as 15 hours past 0 (midnight). 10,000 - 15 = 9,985 Now, convert 9,985 back to hours past midnight: 9,985 = 9,985 imes \frac{1 \text{ hour}}{3600 \text{ seconds}} = 2,829.17 \text{ hours} Since the time is more than 24 hours, we need to subtract multiples of 24 hours to get the correct time on a 24 -hour clock: 2,829.17 - 24 \times 120 = 2,829.17 - 2,880 = - 50.83 \text{ hours} Since the time is negative, we need to add 24 hours: 24 - 50.83 = 13.17 \text{ hours} Convert 13.17 hours to a 24 -hour clock: 13.17 \text{ hours} = 13 \text{ hours} + 0.17 \times 60 \text{ minutes} = 13 \text{ hours} + 10.2 \text{ minutes} So, 10,000 hours prior to 15:00 is 13:00 and 10.2 minutes before the next hour.
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