1. Convert the ffl octal numbers into denary number

a) 1527
b) 21 364

2. Convert the ffl denary numbers into binary numbers
a) 578
b) 709

3. Calculate the follwing using the octal system.
a) 704 + 147
b) 652 - 406
c) 657 * 4
d) 754/6
Thanks

1. To convert octal numbers to denary (decimal) numbers:

a) Convert the octal number 1527 to decimal:
1 * (8^3) + 5 * (8^2) + 2 * (8^1) + 7 * (8^0)
= 1 * 512 + 5 * 64 + 2 * 8 + 7 * 1
= 512 + 320 + 16 + 7
= 855

So, the octal number 1527 is equivalent to 855 in decimal.

b) Convert the octal number 21 364 to decimal:
2 * (8^4) + 1 * (8^3) + 3 * (8^2) + 6 * (8^1) + 4 * (8^0)
= 2 * 4096 + 1 * 512 + 3 * 64 + 6 * 8 + 4 * 1
= 8192 + 512 + 192 + 48 + 4
= 8948

So, the octal number 21 364 is equivalent to 8948 in decimal.

2. To convert decimal numbers to binary:

a) Convert the decimal number 578 to binary:
Divide the decimal number by 2 successively until the quotient becomes 0:
578 ÷ 2 = 289, Remainder = 0
289 ÷ 2 = 144, Remainder = 1
144 ÷ 2 = 72, Remainder = 0
72 ÷ 2 = 36, Remainder = 0
36 ÷ 2 = 18, Remainder = 0
18 ÷ 2 = 9, Remainder = 0
9 ÷ 2 = 4, Remainder = 1
4 ÷ 2 = 2, Remainder = 0
2 ÷ 2 = 1, Remainder = 0
1 ÷ 2 = 0, Remainder = 1

The binary representation is read from the bottom up, so 578 in decimal is equivalent to 1001000010 in binary.

b) Convert the decimal number 709 to binary:
Follow the same process as above:
709 ÷ 2 = 354, Remainder = 1
354 ÷ 2 = 177, Remainder = 0
177 ÷ 2 = 88, Remainder = 1
88 ÷ 2 = 44, Remainder = 0
44 ÷ 2 = 22, Remainder = 0
22 ÷ 2 = 11, Remainder = 0
11 ÷ 2 = 5, Remainder = 1
5 ÷ 2 = 2, Remainder = 0
2 ÷ 2 = 1, Remainder = 0
1 ÷ 2 = 0, Remainder = 1

Therefore, 709 in decimal is equal to 1011000101 in binary.

3. Calculations using the octal system:

a) Calculate the sum of 704 and 147 in octal:
704 + 147 = 1153

So, the sum of 704 and 147 in octal is 1153.

b) Calculate the difference between 652 and 406 in octal:
652 - 406 = 246

So, the difference between 652 and 406 in octal is 246.

c) Calculate the product of 657 and 4 in octal:
657 * 4 = 2514

So, the product of 657 and 4 in octal is 2514.

d) Calculate the division of 754 by 6 in octal:
754 ÷ 6 = 144.1666 (in decimal)

So, the division of 754 by 6 in octal is approximately equal to 144.1666 in decimal.