Question

Could someone help me with these please?
Also, what significance does "signed" vs "unsigned" mean in these cases below?
Some steps would be very helpful.
Thanks for helping me understand!

1. Convert the decimal number to signed 8-bit binary: -35
2. Convert the unsigned 8-bit hexadecimal to unsigned 8-bit binary: 0x80
3. Convert the decimal number to signed 8-bit binary: 127
4. Convert the decimal number to signed 8-bit binary: -100
5. Convert the signed 8-bit binary number to decimal: 1010 1010

Answer 1

Hi, please find the answers below:

When we represent, a number in its decimal form, we generally represent the unsigned form as there is no mention of a positive or negative number. But, in reality, we need to represent signed numbers while working with circuits or hardware, so we need to mention the sign value of the binary. This is called signed form. But we don't have +,- in binary, so we use the MSB(most significant bit). If MSB is 0 it means +ve. If MSB is 1 it means -ve.

1. -35 to signed 8-bit binary:

In 8-bit binary, the most significant bit((MSB) denotes the sign of the number. 0 is for +ve and 1 is for -ve.

binary for 35 is 00100011

covert to 1's complement: 11011100 and add 1 to it: 11011101 which is a 2's compliment. Here the first bit (MSB) which is 1 indicates that the number is a negative number.

2. Unsigned 8-bit hexadecimal to unsigned 8-bit binary: 0x80

0x80 is simply 80 in terms of hexadecimal. To convert hexadecimal to binary we need to get the binary form of each bit in hexadecimal.

So for 0 in hexadecimal, the binary equivalent is 0000

for 8 in hexadecimal, the binary equivalent is 1000

Then, for 0x80 hexadecimal number, it's equivalent unsigned 8-bit binary is 10000000.

3. Convert the decimal number to signed 8-bit binary: 127

The binary representation of decimal value 127 is 01111111. As it is a positive number, no need for any extra modifications.

4. Convert the decimal number to signed 8-bit binary: -100

The binary representation of decimal value 100 is 01100100. Convert the binary value to it's 2's complement form.

Firstly, invert all the bits: 10011011. Add 1 to the last bit: 10011100.

The signed 8-bit representation of -100 is 10011100. The first bit which is 1 represents the number is negative.

5. Convert the signed 8-bit binary number to decimal: 1010 1010

As the given binary starts with 1 it is a negative number. So, first invert all the bits of the binary.

This will result in 01010101. Then, add a 1 to the last bit, which gives 01010110.

Now the decimal equivalent of 01010110 is 86. As it is a negative number, add the sign. This results in -86.