a. What is the range of unsigned integer numbers that can be represented with 4

Question

a. What is the range of unsigned integer numbers that can be represented with

4 bits

8 bits

32 bits

n bits

b. What is the range of numbers in signed magnitude format that can be represented with

4 bits

8 bits

32 bits

n bits

c. What is the range of integers in signed 2’s complement that can be represented with

4 bits

8 bits

32 bits

n bits

d. What is the range of decimal floating point numbers (IEEE 754 representation) that can be represented with

32 bits

64 bits

e. Explain why the bias for the exponent in the IEEE754 has the value: 2k-1 – 1 ?

With understandable explanations please, Thank you so much.

Explanation / Answer

a)What is the range of unsigned integer numbers that can be represented with

4 bit

0 -( 24-1)

0 - 15

8 bit

0 - 28

32 bit

0 - 232

n bit

0 - 2 n

c) What is the range of numbers in signed 2's Complement format that can be represented with

- 2n - 1 and + (2n - 1 - 1).

4 bit

-8 to +7

8 bit

-128 to +127

32 bit

231- (2 31-1)

n bit

2n-1 - (2n-1-1)

d.. What is the range of decimal floating point numbers (IEEE 754 representation) that can be represented with

32 bit

23 bit integer part and 8 bit decimal part and 1 sign bit

52 bit integer part and 11 bit exponent part and 1 sign bit

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