Electronics and Communication Engineering - Digital Electronics - Discussion

How to convert a signed binary two's complement?
1110 0101(2) to an integer in decimal system (in base 10)

1. Is this a positive or a negative number?
In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.
1110 0101 is the binary representation of a negative integer, on 8 bits.


2. Get the binary representation in one's complement:
* Run this step only if the number is negative *
Subtract 1 from the binary initial number:
1110 0101 - 1 = 1110 0100


2. Get the binary representation of the positive (unsigned) number:
* Run this step only if the number is negative *
Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1110 0100) = 0001 1011


3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

27
0
26
0
25
0
24
1
23
1
22
0
21
1
20
1

4. Multiply each bit by its corresponding power of 2 and add all the terms up:
0001 1011(2) = (0 * 27 + 0 * 26 + 0 * 25 + 1 * 24 + 1 * 23 + 0 * 22 + 1 * 21 + 1 * 20)(10) = (0 + 0 + 0 + 16 + 8 + 0 + 2 + 1)(10) = (16 + 8 + 2 + 1)(10) = 27(10).

5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1110 0101(2) = -27(10).

Please understand the question?
The question is saying that the given binary number 11100101 is in already 2's complement form, then how can we write 11100101 in decimal format?

Ans: Left most digit is 1 means it should be a negative number (A/C to question)
1= -ve
0= +ve

step_1------->substract 1 from 11100101 to get 1's complement form
we will get 1's form = 11100100.

step_2--------> Now reverse each digit of 11100100 to get original number in binary
we will get 00011011=27.

step_3--------> so answer will be -27.

Explanation and answer are wrong.

Number with Most Significant digital represents a negative number i.e.
-1*128+1*64+1*32+0*16+0*8+1*4+0*2+1*1.
=-128+64+32+4+1=-27 (which is original number).

Now, 2's complement of the number will be:
1's C: 00011010.
2's C: 00011011.

Binary Equivalent: 16+8+2+1=27 (which is required answer).

At all many have a doubt for the negative sign doubt so I ll try to solve it.

In digital electronics the MSB bit (the leftmost bit) is the sign bit and its negative if it is set to 1 or if it is set to 0 it is positive. So look at the MSB perform the operation and represent it as positive or negative depending on the sign bit.

I think this negative sign has been confirmed from the MSB and LSB bits of the given number and not the 1's complement number.

After finding answer through the appropriate orocedure as discuss above, check the given number, and give the particilar +ve or -ve sign to the answer. Thats it.

2's com -11100101. Then 1's com is 11100101-1=1100100.

Then the required binary no is 0011011. According to binary to decimal conversion the position value is 128, 64, 32, 16, 8, 4, 2, 1 here binary 1 is present in 16+8+2+1=27.

It is used in short form that you are seeing 16+8+2+1. It is basically the conversion of binary in decimal where 1 is there we add all that positions by taking 2^4+2^8+2^1+2^0 power here represents the position of bits.

Is the 1's complement and 2's complement are the complement each other?

Because the procedure is same, if we find the 2's complement we use the same procedure and here also use the same procedure.

Here they just asked that 2's compliment of the decimal number is 11100101 so what is that decimal number?

If you see MSBbit is one so the decimal number should be in negative not positive.

The negative number always represent in 2's complement form. So after calculating 2's complement of the above binary number, it is always negative. So the D option is correct.