Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Sure! Let's convert each of the given decimal numbers into their octal equivalents step by step.
a) Convert 67 to octal:
1. Divide 67 by 8, the base of the octal number system.
[tex]\( 67 \div 8 = 8 \)[/tex] remainder [tex]\( 3 \)[/tex]
2. Next, divide the quotient (8) by 8.
[tex]\( 8 \div 8 = 1 \)[/tex] remainder [tex]\( 0 \)[/tex]
3. Finally, divide the next quotient (1) by 8.
[tex]\( 1 \div 8 = 0 \)[/tex] remainder [tex]\( 1 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 103 \)[/tex]
So, [tex]\( 67 \)[/tex] in decimal is [tex]\( 103 \)[/tex] in octal.
b) Convert 105 to octal:
1. Divide 105 by 8.
[tex]\( 105 \div 8 = 13 \)[/tex] remainder [tex]\( 1 \)[/tex]
2. Next, divide the quotient (13) by 8.
[tex]\( 13 \div 8 = 1 \)[/tex] remainder [tex]\( 5 \)[/tex]
3. Finally, divide the next quotient (1) by 8.
[tex]\( 1 \div 8 = 0 \)[/tex] remainder [tex]\( 1 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 151 \)[/tex]
So, [tex]\( 105 \)[/tex] in decimal is [tex]\( 151 \)[/tex] in octal.
c) Convert 571 to octal:
1. Divide 571 by 8.
[tex]\( 571 \div 8 = 71 \)[/tex] remainder [tex]\( 3 \)[/tex]
2. Next, divide the quotient (71) by 8.
[tex]\( 71 \div 8 = 8 \)[/tex] remainder [tex]\( 7 \)[/tex]
3. Finally, divide the next quotient (8) by 8.
[tex]\( 8 \div 8 = 1 \)[/tex] remainder [tex]\( 0 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 1073 \)[/tex]
So, [tex]\( 571 \)[/tex] in decimal is [tex]\( 1073 \)[/tex] in octal.
d) Convert 238 to octal:
1. Divide 238 by 8.
[tex]\( 238 \div 8 = 29 \)[/tex] remainder [tex]\( 6 \)[/tex]
2. Next, divide the quotient (29) by 8.
[tex]\( 29 \div 8 = 3 \)[/tex] remainder [tex]\( 5 \)[/tex]
3. Finally, divide the next quotient (3) by 8.
[tex]\( 3 \div 8 = 0 \)[/tex] remainder [tex]\( 3 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 356 \)[/tex]
So, [tex]\( 238 \)[/tex] in decimal is [tex]\( 356 \)[/tex] in octal.
The results are:
- [tex]\( 67 \)[/tex] in decimal is [tex]\( 103 \)[/tex] in octal.
- [tex]\( 105 \)[/tex] in decimal is [tex]\( 151 \)[/tex] in octal.
- [tex]\( 571 \)[/tex] in decimal is [tex]\( 1073 \)[/tex] in octal.
- [tex]\( 238 \)[/tex] in decimal is [tex]\( 356 \)[/tex] in octal.
a) Convert 67 to octal:
1. Divide 67 by 8, the base of the octal number system.
[tex]\( 67 \div 8 = 8 \)[/tex] remainder [tex]\( 3 \)[/tex]
2. Next, divide the quotient (8) by 8.
[tex]\( 8 \div 8 = 1 \)[/tex] remainder [tex]\( 0 \)[/tex]
3. Finally, divide the next quotient (1) by 8.
[tex]\( 1 \div 8 = 0 \)[/tex] remainder [tex]\( 1 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 103 \)[/tex]
So, [tex]\( 67 \)[/tex] in decimal is [tex]\( 103 \)[/tex] in octal.
b) Convert 105 to octal:
1. Divide 105 by 8.
[tex]\( 105 \div 8 = 13 \)[/tex] remainder [tex]\( 1 \)[/tex]
2. Next, divide the quotient (13) by 8.
[tex]\( 13 \div 8 = 1 \)[/tex] remainder [tex]\( 5 \)[/tex]
3. Finally, divide the next quotient (1) by 8.
[tex]\( 1 \div 8 = 0 \)[/tex] remainder [tex]\( 1 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 151 \)[/tex]
So, [tex]\( 105 \)[/tex] in decimal is [tex]\( 151 \)[/tex] in octal.
c) Convert 571 to octal:
1. Divide 571 by 8.
[tex]\( 571 \div 8 = 71 \)[/tex] remainder [tex]\( 3 \)[/tex]
2. Next, divide the quotient (71) by 8.
[tex]\( 71 \div 8 = 8 \)[/tex] remainder [tex]\( 7 \)[/tex]
3. Finally, divide the next quotient (8) by 8.
[tex]\( 8 \div 8 = 1 \)[/tex] remainder [tex]\( 0 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 1073 \)[/tex]
So, [tex]\( 571 \)[/tex] in decimal is [tex]\( 1073 \)[/tex] in octal.
d) Convert 238 to octal:
1. Divide 238 by 8.
[tex]\( 238 \div 8 = 29 \)[/tex] remainder [tex]\( 6 \)[/tex]
2. Next, divide the quotient (29) by 8.
[tex]\( 29 \div 8 = 3 \)[/tex] remainder [tex]\( 5 \)[/tex]
3. Finally, divide the next quotient (3) by 8.
[tex]\( 3 \div 8 = 0 \)[/tex] remainder [tex]\( 3 \)[/tex]
4. The remainders collected from bottom to top form the octal number: [tex]\( 356 \)[/tex]
So, [tex]\( 238 \)[/tex] in decimal is [tex]\( 356 \)[/tex] in octal.
The results are:
- [tex]\( 67 \)[/tex] in decimal is [tex]\( 103 \)[/tex] in octal.
- [tex]\( 105 \)[/tex] in decimal is [tex]\( 151 \)[/tex] in octal.
- [tex]\( 571 \)[/tex] in decimal is [tex]\( 1073 \)[/tex] in octal.
- [tex]\( 238 \)[/tex] in decimal is [tex]\( 356 \)[/tex] in octal.
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
