Question

1a) 0xCAFE can be written in decimal (base 10) as:

1b)

The decimal number -94 can be expressed (in 8 bits)

Using signed magnitude representation as:

Using one's complement representation as:

Using two's complement representation as:

Using excess-M representation (with the appropriate value of M) as:

1c)

Using the simple floating point model (1-bit sign, 5-bit biased exponent, and 8-bit significand), the number -0.125 (decimal) can be expressed as:

(Do not use spaces or any English text. Provide only the bit pattern.)

1d)

Which of the following (select all that apply) have occurred in this computation using 2's complement representation with 8-bit binary: 32 (decimal) - 6 (decimal):

Options:

1)

Carry

2)

Overflow

3)	Neither Carry nor Overflow

Answer 1

1 a)

CAFE)₁₆ = (12 × 16³) + (10 × 16²) + (15 × 16¹) + (14 × 16⁰) = (51966)₁₀

b)

I)01011110

ii)10100001

iii)10100001+1=10100010

1 c) 1 01100 00000000

Explanation:-

0.125₍₁₀₎ =

0.001₍₂₎ =

0.001₍₂₎ × 2⁰ =

1₍₂₎ × 2^-3

Sign: 1 (a negative number)

Exponent (unadjusted): -3

Mantissa (not normalized):
1

Adjust the exponent.

Use the 8 bit excess/bias notation:

Exponent (adjusted) =

Exponent (unadjusted) + 2^(5-1) - 1 =

-3 + 2^(5-1) - 1 =

(-3 + 15)₍₁₀₎ =

12₍₁₀₎

₌₀₁₁₀₀

Mantissa (normalized) =

1 000 0000 =

000 0000

Answer;-

1 01100 00000000

1d)

32 -6

32+(-6)

32=00100000

-6=1111 1010

32+(-6)=0010 0000 + 1111 1010=1 0001 1010

Discard carry answer:- 0001 1010

1) carry