Final answer:
Binary number 1011101 converts to 93 in base ten and 275 in base eight. Binary number 10110 converts to 31 in base seven. The conversion for 1000111 was not provided due to incomplete information.
Step-by-step explanation:
To convert the binary number 1011101 to a base ten number, we proceed as follows:
- 1 x 2^6 = 64
- 0 x 2^5 = 0
- 1 x 2^4 = 16
- 1 x 2^3 = 8
- 1 x 2^2 = 4
- 0 x 2^1 = 0
- 1 x 2^0 = 1
Add the values: 64 + 16 + 8 + 4 + 1 = 93. Therefore, 1011101 in binary is 93 in base ten.
To convert 1011101 to a base eight number:
- Group the binary digits into sets of three from right to left: 10 111 101.
- Convert each set to base eight: 2, 7, 5.
Thus, 1011101 in base two is 275 in base eight.
For the binary number 10110 to base seven:
- Convert the binary number to base ten: 1 x 2^4 + 0 x 2^3 + 1 x 2^2 + 1 x 2^1 + 0 x 2^0 = 16 + 0 + 4 + 2 = 22.
- Divide 22 by 7, the quotient is 3 and the remainder is 1, so the last digit in base seven is 1.
- Divide the quotient 3 by 7, the new quotient is 0 and the remainder is 3, so the next digit is 3.
Therefore, 10110 in binary is 31 in base seven.
The final conversion for the number 1000111 was not completed due to incomplete instruction.