the table to the right shows the digits of th...
the table to the right shows the digits of the octal system (base eight) and their equivalents in the binary system (base two). use the table to fill in the blanks below. (a) write 11001010111_two in the octal system. 11001010111_two = _eight (b) write 724_eight in the binary system. 724_eight = _two
Answer
# Explanation:
## Step1: Group binary digits for (a)
Group the binary number 11001010111 from right - to - left in groups of 3. If the left - most group has less than 3 digits, add leading 0s. So, 11001010111 becomes 001 100 101 011.
## Step2: Convert groups to octal for (a)
Using the octal - binary conversion table, 001 in binary is 1 in octal, 100 is 4, 101 is 5, and 011 is 3. So, 11001010111₂ = 1453₈.
## Step3: Convert octal digits to binary for (b)
For each digit in 724₈, convert it to a 3 - digit binary number. 7 in octal is 111 in binary, 2 is 010, and 4 is 100. So, 724₈ = 111010100₂.
# Answer:
(a) 1453
(b) 111010100