Convert the following twos complement binary numbers into de

Convert the following two\'s complement binary numbers into decimal (base 10). %1001 0101 %0100 1110 %1011 1000 % 1000 0101

Solution

1)

10010101 = 149

A             Power of 2:         27           26           25           24           23           22           21           20

B             Place value (A result):    128         64           32           16           8              4              2              1

C             Entered binary digit:       1              0              0              1              0              1              0              1

D             Product of B * C:              128         0              0              16           0              4              0              1

E              Cumulative total of D:    128         128         128         144         144         148         148         149

2)01001110=78

According to my calculations, the binary number 10011102 is equivalent to the decimal number 78. The following binary to decimal conversion chart shows how I arrived at my result.

A             Power of 2:         26           25           24           23           22           21           20

B             Place value (A result):    64           32           16           8              4              2              1

C             Entered binary digit:       1              0              0              1              1              1              0

D             Product of B * C:              64           0              0              8              4              2              0

E              Cumulative total of D:    64           64           64           72           76           78           78

3)

10111000=184

According to my calculations, the binary number 101110002 is equivalent to the decimal number 184. The following binary to decimal conversion chart shows how I arrived at my result

A             Power of 2:         27           26           25           24           23           22           21           20

B             Place value (A result):    128         64           32           16           8              4              2              1

C             Entered binary digit:       1              0              1              1              1              0              0              0

D             Product of B * C:              128         0              32           16           8              0              0              0

E              Cumulative total of D:    128         128         160         176         184         184         184         184

4)

10000101=133

According to my calculations, the binary number 100001012 is equivalent to the decimal number 133. The following binary to decimal conversion chart shows how I arrived at my result.

A             Power of 2:         27           26           25           24           23           22           21           20

B             Place value (A result):    128         64           32           16           8              4              2              1

C             Entered binary digit:       1              0              0              0              0              1              0              1

D             Product of B * C:              128         0              0              0              0              4              0              1

E              Cumulative total of D:    128         128         128         128         128         132         132         133