1. Convert 0X8000 1C61 from the 32-bit sign and magnitude format to a decimal nu

Question

1. Convert 0X8000 1C61 from the 32-bit sign and magnitude format to a decimal number

2. Convert 0x8000 2305 from the 32-bit sign and magnitude format to a decimal number.

3. Convert 0x0000 1290 from the 32-bit one's complement format to a decimal number.

4. Convert 0xFFFF DCF0 from the 32-bit one's complement format to a decimal number.

5. Convert 0x0000 1A8E from the 32-bit two's complement format to a decimal number.

6. Convert 0xFFFF F25F from the 32-bit two's complement format to a decimal number.

Explanation / Answer

leftmost bit indicates sign which is 1 for negative numbers and 0 for positive numbers

1. Convert 0X8000 1C61 from the 32-bit sign and magnitude format to a decimal number

In sign and magnitude representation leftmost bit represents sign and rest of the bits represent magnitude. Therefore 0X8000 1C61 is a negative number as leftmost bit is 1.

Binary representation of this number is

1000 0000 0000 0000 0001 1100 0110 0001

Eq. decimal number is -7265

2. Convert 0x8000 2305 from the 32-bit sign and magnitude format to a decimal number.

0x8000 2305 is a negative number as the leftmost bit is 1.

binary representation of this number is 1000 0000 0000 0000 0010 0011 0000 0101

Eq. Decimal number is -8965

3. Convert 0x0000 1290 from the 32-bit one's complement format to a decimal number.

In one's Complement number system, positive numbers are represented as regular binary numbers while negative numbers are represented by inverting all bits of binary representation of corresponding +ve number.

0x0000 1290 is a positive number as leftmost bit is 0.

Binary representation of this number is 0000 0000 0000 0000 0001 0010 1001 0000

Eq. Decimal number is +4752

4. Convert 0xFFFF DCF0 from the 32-bit one's complement format to a decimal number.

0xFFFF DCF0 is a negative number as leftmost bit is 1.

Binary representation is 1111 1111 1111 1111 1101 1100 1111 0000

Magnitude of the Decimal number is obtained by inverting all the bits which is

0000 0000 0000 0000 0010 0011 0000 1111

Eq. Decimal number is -8975

5. Convert 0x0000 1A8E from the 32-bit two's complement format to a decimal number.

In Two's complement number system, +ve numbers are represented as regular binary numbers while negative numbers are represented by inverting all the bits of corresponding +ve binary number and then adding 1.

0x0000 1A8E is a +ve number as leftmost bit is 0.

Binary representation is 0000 0000 0000 0000 0001 1010 1000 1110

Eq. Decimal number is +6798

6. Convert 0xFFFF F25F from the 32-bit two's complement format to a decimal number.

0xFFFF F25F is a -ve number as leftmost bit is 1.

Binary representation is 1111 1111 1111 1111 1111 0010 0101 1111

We get Decimal number by flipping all the bits and then adding 1.

which is

0000 0000 0000 0000 0000 1101 1010 0000

                                                                  +1

0000 0000 0000 0000 0000 1101 1010 0001

Eq. Decimal number is -3489

Please let me know in case of any doubt.

Thanks

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