Question

Consider the eight bit signed binary number 1110 0101. Convert it to signed decimal from assuming the signed binary number is represented using signed magnitude.

1110 0101

Answer 1

-101

Step-by-step explanation:

In the given number 1110 0101 , the left most bit represents the sign. If leftmost bit is 1 it is negative number and if it is 0 it is positive number. Here leftmost bit 1 is reserved for sign and the remaining bits (110 0101) represents the magnitude. If you want to convert that into decimal you have to Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

110 0101(2) =

(1 * pow(2,6)+ 1 *pow(2,5)+ 0 *pow(2,4)+ 0 *pow(2,3)+ 1 *pow(2,2)+ 0 *pow(2,1)+ 1 * pow(2,0))(10) =

(64 + 32 + 0 + 0 + 4 + 0 + 1)(10) =

(64 + 32 + 4 + 1)(10) =

101(10)