Question

Convert each of the following 8-bit numbers to hexadecimal and then to octal a) 10011101 b) 00010101 c) 11100110 d) 01101001

Answer 1

Answer:

a) 10011101₂ = 9D₁₆ or 235₈

b) 00010101₂ = 15₁₆ or 025₈

c) 11100110₂ = E6₁₆ or 346₈

d) 01101001₂ = 69₁₆ or 151₈

Explanation:

An hexadecimal is a group of 4bits while an octal is a group of 3 bits. They are represented in the table below;

Table for conversion;

Octal   =>    binary

0         =>     000

1          =>     001

2          =>    010

3          =>    011

4          =>    100

5          =>    101

6          =>    110

7          =>    111

Hexadecimal   => binary

0                      =>     0000

1                       =>     0001

2                      =>     0010

3                      =>     0011

4                      =>     0100

5                      =>     0101

6                      =>     0110

7                      =>     0111

8                      =>     1000

9                      =>     1001

A                      =>    1010

B                      =>    1011

C                      =>    1100

D                      =>    1101

E                      =>    1110

F                      =>    1111

(a)

(i) Convert 10011101 to hexadecimal

Step 1: Starting from the right, split the number into groups of 4s as follows;

1001   1101

Step 2: Convert each of the groups into its equivalent hexadecimal using the table above;

1001 = 9

1101 = D

Step 3: Put them together;

1001 1101₂ = 9D₁₆

(ii) Convert 10011101 to octal

Step 1: Starting from the right, split the number into groups of 3s as follows;

10  011  101

Step 2: The last group (10) in the result of step 1 above has only 2 bits. Therefore, add zero to its left to make it 3 bits as follows;

010  011  101

Step 3: Convert each of the groups into its equivalent octal using the table above;

010 = 2

011 = 3

101 = 5

Step 4: Put them together;

10 011 101₂ = 235₈

(b)

(i) Convert 00010101 to hexadecimal

Step 1: Starting from the right, split the number into groups of 4s as follows;

0001   0101

Step 2: Convert each of the groups into its equivalent hexadecimal using the table above;

0001 = 1

0101 = 5

Step 3: Put them together;

0001 0101₂ = 15₁₆

(ii) Convert 00010101 to octal

Step 1: Starting from the right, split the number into groups of 3s as follows;

00  010  101

Step 2: The last group (00) in the result of step 1 above has only 2 bits. Therefore, add zero to its left to make it 3 bits as follows;

000  010  101

Step 3: Convert each of the groups into its equivalent octal using the table above;

000 = 0

010 = 2

101 = 5

Step 4: Put them together;

00 010 101₂ = 025₈

(c)

(i) Convert 11100110 to hexadecimal

Step 1: Starting from the right, split the number into groups of 4s as follows;

1110  0110

Step 2: Convert each of the groups into its equivalent hexadecimal using the table above;

1110 = E

0110 = 6

Step 3: Put them together;

1110 0110₂ = E6₁₆

(ii) Convert 11100110 to octal

Step 1: Starting from the right, split the number into groups of 3s as follows;

11 100 110

Step 2: The last group (11) in the result of step 1 above has only 2 bits. Therefore, add zero to its left to make it 3 bits as follows;

011 100 110

Step 3: Convert each of the groups into its equivalent octal using the table above;

011 = 3

100 = 4

110 = 6

Step 4: Put them together;

11 100 110₂ = 346₈

(d)

(i) Convert 01101001 to hexadecimal

Step 1: Starting from the right, split the number into groups of 4s as follows;

0110 1001

Step 2: Convert each of the groups into its equivalent hexadecimal using the table above;

0110 = 6

1001 = 9

Step 3: Put them together;

0110 1001₂ = 69₁₆

(ii) Convert 01101001 to octal

Step 1: Starting from the right, split the number into groups of 3s as follows;

01 101 001

Step 2: The last group (01) in the result of step 1 above has only 2 bits. Therefore, add zero to its left to make it 3 bits as follows;

001 101 001

Step 3: Convert each of the groups into its equivalent octal using the table above;

001 = 1

101 = 5

001 = 1

Step 4: Put them together;

01 101 001₂ = 151₈