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3 - What decimal number does the bit pattern 11001100 represent if it is a: •...

3 - What decimal number does the bit pattern 11001100 represent if it is a:
• [1 pts] unsigned integer?
• [1 pts] sign-magnitude integer?
• [1 pts] two's complement integer?

4 - What decimal number does the bit pattern 00110011 represent if it is a:
• [1 pts] unsigned integer?
• [1 pts] sign-magnitude integer?
• [1 pts] two's complement integer?

If you could show work that would be helpful as I have to do that to get credit. Thanks.

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Answer #1

3 - bit pattern 11001100

  • unsigned integer

11001100(2) = (1 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10)

11001100(2) = (128 + 64 + 0 + 0 + 8 + 4 + 0 + 0)(10)

11001100(2) = (128 + 64 + 8 + 4)(10)

11001100(2) = 204(10)

  • sign-magnitude integer

  In a signed binary, first bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive.
This bit does not count when calculating the absolute value.

1001100(2) = (1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10)

1001100(2) = (64 + 0 + 0 + 8 + 4 + 0 + 0)(10)

1001100(2)= (64 + 8 + 4)(10)

1001100(2)= 76(10)

Adjust the sign of the integer number by the first digit (leftmost) of the signed binary.

  11001100(2) = -76(10)

  • two's complement integer

  In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

11001100 is the binary representation of a negative integer, on 8 bits.

Run this step only if the number is negative

Subtract 1 from the binary initial number:

11001100 - 1 = 11001011

  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:

!(1100 1011) = 0011 0100

00110100(2) = (0 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10)

00110100(2) = (0 + 0 + 32 + 16 + 0 + 4 + 0 + 0)(10)

00110100(2) = (32 + 16 + 4)(10)

00110100(2) = 52(10)

Adjust the sign of the integer number by the first digit (leftmost) of the signed binary.

  00110100(2) = -52(10)

4 - bit pattern 00110011

  • unsigned integer

00110011(2) = (1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10)

00110011(2) = (32 + 16 + 0 + 0 + 2 + 1)(10)

00110011(2) = (32 + 16 + 2 + 1)(10)

00110011(2)= 51(10)

  • sign-magnitude integer

In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

00110011 is the binary representation of a positive integer, on 8 bits.

0110011(2) = (1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10)

0110011(2) = (32 + 16 + 0 + 0 + 2 + 1)(10)

0110011(2) = (32 + 16 + 2 + 1)(10)

0110011(2)= 51(10)

Adjust the sign of the integer number by the first digit (leftmost) of the signed binary.

00110011(2) = 51(10)

  • two's complement integer

   In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

00110011 is the binary representation of a positive integer, on 8 bits.

00110011(2) = (1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10)

00110011(2) = (32 + 16 + 0 + 0 + 2 + 1)(10)

00110011(2) = (32 + 16 + 2 + 1)(10)

00110011(2)= 51(10)

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