25 Express each decimal number as an 8-bit number in the 2\'s complement form: a

Question

25 Express each decimal number as an 8-bit number in the 2's complement form: a. +12 (5 pts) b. -68 (5 pts) c. +101 (5 pts) d. -125 (5 pts) 28 Determine the decimal value of each signed binary number in the 2's complement form: 30 Determine the values of the following single-precision floating-point numbers: b. 0 11001100 10000111110100100000000 (5 pts) Section 2-7 Arithmetic Operations with Signed Numbers 35 Multiply 01101010 by 11110001 in the 2's complement form. (5 pts) 36 Divide 01000100 by 00011001 in the 2's complement form. (5 pts) Section 2-8 Hexadecimal Numbers 40 Convert each decimal number to hexadecimal g. 4019 (5 pts) h. 6500 (5 pts) 41 Perform the following additions: b. A016 6B16 (5 pts) c. FF16 BB16 (5 pts) 42 Perform the following subtractions: b. C816-3A16 (5 pts) c. FD16- 8816(5 pts)

Explanation / Answer

25)

a)   +25

convert 25 to 8 bit binary number : 11001

2's complememt of a positive number is same as it binary reprentation.

2's complememt of + 25 : 00011001 (pad with zeros to make 8 bit)

b) -68

convert 68 to 8 bit binary number : 11000100

Negate the number by inverting the bits : 00111011

add 1 to the inverted number : 00111011

                                                 +     1

                                      -----------------------

                                             00111100   => 2's complement

c) + 101

convert 101 to binary : 1100101

2's complemet : 01100101

d) -125

1convert to binary : 00111101

invert : 11000010

add 1 :    11000010 => 2's complement

28   )10111111

notice that the number is negative as MSB is 1.

inverse the number to get magnitude:     01000000

Add 1 : 01000001

Convert to decimal   = 1*27 + 1*20 = 128+1 =129

Answer is : -129

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