Question

Assume a computer is using signed magnitude base 2 representation to store 8-bit values. Further, assume you have a program which can display the contents of 1-byte memory locations. However, the program displays hex (as a shorthand) instead of binary. What decimal values are represented by the following:

(a) C3

(b) 6E

Repeat the above, but assume the numbers are stored as 8-bit 2’s complement base 2.

Answer 1

In Signed Magnitude Representation of a n bit number we have one bit reserved that depicts the sign and rest n-1 bits tell the magnitude of that number .

SO MSB bits determined the Sign of the Number .

If MSB=0 Then number is Positive , if MSB = 1 then number is negative

Now we have hexadecimals number . So to get equivalent first write them in 8 bits binary

We have

1. C3 = 1100 0011

Now As MSB is 1 so Number is negative

Magnitude = 1000011 = 67

Hence Decimal value of C3 = -67

2. 6E = 01101110

Now As MSB is 0 so Number is positive

Magnitude = 01101110 = 110

Hence Decimal value of 6E = +110

This is how you can find equivalent decimal value for the given hexadecimal represented in the Signed Magnitude Representation

Now we have 2's complement Notation :

In This notation Positive number are represented same as in normal binary so there is no change but when we represent a negative numebr then we take 2's complement of its positive value only .

Here also MSB represent the Sign

To get Magnitude in case of positive number just get the equivalent decimal of 8 bit binary

But in Negative Number decimal value is equal to 2's complement of the Given 8- Bit binary

Lets see for given Numbers

.1. C3 = 1100 0011

Now As MSB is 1 so Number is negative

Magnitude = 2's complement ( 11000011)= 00111101 = 61

Hence Decimal value of C3 = -61

2. 6E = 01101110

Now As MSB is 0 so Number is positive

Magnitude ( no need of 2's complement as number is +ve)=  1101110 = 110

Hence Decimal value of 6E = +110

This how 2's complement notation works and we get equivalent decimal

Thank you

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