Question

The standard way of notating negative numbers in English is sign and magnitude. Basically, put a

minus sign in front of a number if it is negative. This can be done in binary as well. For example,

in 4 bits, the sign and magnitude encoding for -5 is 1101, where the leftmost 1 indicates a negative

number. Sign and magnitude encoding is used in IEEE floating point types.

What is the range (minimum to maximum) of integers that can be encoded into 8 bits using sign and

magnitude encoding?

Answer 1

What is the range (minimum to maximum) of integers that can be encoded into 8 bits using sign and magnitude encoding?

Ans: using sign and magnitude encoding, the range of number is:

-2^(n-1) -1 to  +2^(n-1) -1

Here n=8 so -2⁷-1 to  +2⁷ -1

^{The minimum number is -127 (1 1111111) first bit is sign bit and it is 1 for the negative number and 0 for a positive number}

^{Maximum number is +127 (0 1111111)}