Help with 2&3 What are the decimal values of each of the following binary number

Question

Help with 2&3

What are the decimal values of each of the following binary numbers if you interpret them as 2's complement integers? 1111 1111 0000 1010 1111 1111 1101 1111 0111 1111 1101 1111 0101 0101 0101 0101 Add your answers in hw1.txt. Take the same bit patterns from problem 1 and interpret them as the following representations. Provide their value as decimal numbers. Unsigned Sign Magnitude 1's complement Biased Add your answers to hw1.txt. For each of the bit lengths and number representations below, list the binary encodings and values of the possible numbers closest to infinity and to infinity. (For each of the three parts to this question, you will provide two binary strings and two corresponding decimal numbers.) A nibble (4 bits) using two's compliment. A byte using sign-magnitude. A byte using one's compliment. Add your answers to hw1.txt

Explanation / Answer

Answer 1

     1111 1111 0000 1010

+                                             1

Ans = 11110110 =-246

Answer 2

For example I am taking first sub part a

Number is 1111 1111 0000 1010 which is in 2’s compliment

Decimal equivalent is = -246 which is signed

Unsigned number = 1111 0110 = 128+64+32+16+4+2= 246

Sign magnitude = negative

1’s compliment = 0000 0000 1111 0110

Biased = given 8 bits bias values by 2^7(128)

True value =7

Add bias = 7+128 = 135

Unsigned value = +135

So value = 1000 0111

Answer 3

Nibble is binary representation in 4 bits

For example for a number 0101

1’s compliment= 1010

2’s compliment = 1010+1 = 1011

Byte using sign magnitude = 1010 0101 is negative because starts with 1

Byte using 1’s compliment = 0101 1010

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