Digital Logic and Data Manipulation: Conversion Exercises and Applications

Digital Logic and Data Manipulation

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Section A
Question 1
Convert the Binary numbers to Octal numbers:
Step: Create a group of three digits from the binary number and then convert it into
an octal number using the table above. Then put the equivalent value of the grouped
digits.
A. 110110110
(110) (110) (110) = (666)8 (110= 6)
B. 1001001
(001)(001) (001) = (111)8 (001= 1)
C. 10010110
(010) (010) (110) = (226)8 (010= 2, 110= 6)
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Question 2
Convert the Binary numbers to Decimal numbers:
Step: Multiply each digit of the given binary number to the base 2 having its power
as it place value.
A. 11101011
= 1x 27 + 1x 26+ 1x 25 + 0x 24+ 1x 23 + 0x 22+ 1x 21 + 1x 20
= 128+64+32+8+2+1 = (235)10
B. 01100101
= 0x 27 + 1x 26+ 1x 25 + 0x 24+ 0x 23 + 1x 22+ 0x 21 + 1x 20
= 64+ 32+ 4 + 1= (101)10
C. 01010101
= 0x 27 + 1x 26+ 0x 25 + 1x 24+ 0x 23 + 1x 22+ 0x 21 + 1x 20
= 64+ 16+ 4+ 1 = (85)10
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Question 3
Steps
Step 1: Make a group of four digits starting from the rightmost digit
Step 2: Find equivalent value to that group from the table given above.
Step 3: If in the last group there is less digit than four. Complete it by putting zeros
on the left side.
Convert the Binary numbers to Hexadecimal numbers:
A. 10001001
(1000)(1001) = (89)16
B. 11000111
(1100)(0111)= (C7)16
C. 01101010
(0110) (1010)= (6A)16
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Figure 1: Binary-Hexadecimal
conversion table

Question 4
Steps
Step 1: Find equivalent of the each given hexadecimal digits from the table given
above. And join them to get the binary equivalent.
Step 2: Now make a group of three digits from the binary equivalent starting from the
rightmost side of the number.
Step 3: If any of the digits is not grouped with three digits on the left side then put
zero on its left side to complete the group.
Step 4: Find the equivalent octal value of the created groups from the table below
and join then to get the octal number.
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Figure 2: Binary-Hexadecimal
conversion table