Question

1a. 569 (base 10)=_________(base 3) SHOW WORK

1b. 357 (base 9)=___________(base 3) SHOW WORK

1c. 10011100 (base 2)=__________(base 10) SHOW WORK

Answer 1

a)
Divide 569 successively by 3 until the quotient is 0
569/3 = 189, remainder is 2
189/3 = 63, remainder is 0
63/3 = 21, remainder is 0
21/3 = 7, remainder is 0
7/3 = 2, remainder is 1
2/3 = 0, remainder is 2
Read remainders from the bottom to top as 210002
Answer: 210002

b)
first convert 357 of base-9 to deicmal
357
=> 3x9^2+5x9^1+7x9^0
=> 3x81+5x9+7x1
=> 3x81+5x9+7x1
=> 243+45+7
=> 295

Now, let's convert this decimal value of 295 to base-3
Divide 295 successively by 3 until the quotient is 0
295/3 = 98, remainder is 1
98/3 = 32, remainder is 2
32/3 = 10, remainder is 2
10/3 = 3, remainder is 1
3/3 = 1, remainder is 0
1/3 = 0, remainder is 1
Read remainders from the bottom to top as 101221
Answer: 101221

c)
Converting 10011100 to decimal
10011100
=> 1x2^7+0x2^6+0x2^5+1x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x128+0x64+0x32+1x16+1x8+1x4+0x2+0x1
=> 128+0+0+16+8+4+0+0
=> 156
Answer: 156