Question

1. What is the largest decimal number we can represent with a 16 bit two's complement number?

2.

Convert the following signed binary numbers to decimals.

11001        

010011           

1110100           

1100111          

3.

Convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Note if there is an overflow.

7 + 13

Two's complement/binary number for 7:

Two's complement/binary number for 13:

Sum:

Overflow?

4.

Convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Note if there is an overflow.

17 + 25

Two's complement/binary number for 17:

Two's complement/binary number for 25:

Sum:

Overflow?

5. c

onvert the following decimal numbers to 6-bit two's complement binary numbers and add them. Note if there is an overflow.

(-26) + 8

Two's complement/binary number for -26:

Two's complement/binary number for 8:

Sum:

Overflow?

6.

Convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Note if there is an overflow.

31 + (-14)

Two's complement/binary number for 31:

Two's complement/binary number for -14:

Sum:

Overflow?

7.

Convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Note if there is an overflow.

(-19) + (-22)

Two's complement/binary number for -19:

Two's complement/binary number for -22:

Sum:

Overflow?

8.

Convert the following decimal numbers to 6-bit two's complement binary numbers and add them. Note if there is an overflow.

(-2) + (-29)

Two's complement/binary number for -2:

Two's complement/binary number for -29:

Sum:

Overflow?

Answer 1

As we know that in 2's complement Representation ni bits Represent Decimal numbers in the Range: -2 -1 to +(221) Therefore the largest secimal no. that can be represented with a 16 bit two's compliment number - = +2 -1) 3 25-1 = 32768-1 = 32767