Homework Soursesuppose that we ahve the following 8bit binary value 1001101
suppose that we ahve the following 8-bit binary value.
10011011
1) What is the decimal value of this binary word if we interpret it as an unsigned 8-bit integer? Explain your calculation.
2) What is the decimal value of this binary word if we interpret it as a two\'s complement 8-bit integer? Explain your calculation.
3) What is the decimal value of this binary word if we interpret it as a signed-magnitude 8-bit integer? Explain your calculation.
Solution
10011011
1) What is the decimal value of this binary word if we interpret it as an unsigned 8-bit integer? Explain your calculation.
2) What is the decimal value of this binary word if we interpret it as a two\'s complement 8-bit integer? Explain your calculation.
3) What is the decimal value of this binary word if we interpret it as a signed-magnitude 8-bit integer? Explain your calculation.
Solution of 1) - part.
For unsigned binary to decimal conversion we multiply number by 2 powers and then finally add all the result...
1 0 0 1 1 0 1 1
1
0
0
1
1
0
1
1
27
26
25
24
23
22
21
20
128 + 0 + 0 + 16 + 8 + 0 + 2 + 1
= 155
Multiply both the rows by 2’s power add them
The decimal of (10011011)2---------- (155)10
Solution of 2) - part.
For converting it in 2’s complement
Step 1)- first we check the number is +ve or –ve for this we check the left most bit if it is 1 the number is –ve if bit is 0 then number is +ve
In our case first bit is 1 so the number is –ve. But this case for signed magnitude in question you not mention for this..
1
0
0
1
1
0
1
1
Now we change the bit from 1 to 0 and 0 to 1.then what we get.
0
1
1
0
0
1
0
0
Step 2)- now we reverse the bit like 1--à 0 and 0 --à 1 Look below
Multiply both the rows by 2’s power and add them
Then add 1 in right most bit after adding Multiply both the rows by 2’s power add them look below
0
1
1
0
0
1
0
0
Add 1 in right most bit 1
0
1
1
0
0
1
0
1
0 + 64 + 32 + + 0 + 4 + 0 + 1
= (101)
(10011011)2à(01100101)2 2’s complement
Solution of 3) - part.
The signed magnitude represent the binary number with signed the Left most bit is called signed bit if the
Bit is 1 the number is negative if the bit is bit is 0 then the number is positive.
In our case first bit is 1 so the number is –ve
Then left bit is not multiply by 2\'s power but we multiply rest bits with 2’s power and add them
1
0
0
1
1
0
1
1
--
26
25
24
23
22
21
20
0 + 0 + 16 + 8 + 0 + 1 + 0
= -(25)
Calculate the decimal number --
The Left most bit was 1 so the number is –ve .
(10011011)2-------------------------------à -(25)10
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
| 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155 |
