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.
