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
