The best approximation to the value one-tenth that can be represented using 8-bit floating-point format described in figure $1.24$ :

Convert the given value in the binary representation.

Copy the bit pattern into the mantissa field from left to right, start with 1.

Copy the bit pattern into the mantissa field from left to right, start with 1.

The exponential field is determined by assuming the pattern of mantissa field with a radix at its left and it obtains the original binary number by determining the number of bits and direction of radix that must be moved.

The remaining three bits represent the exponential field that is shown in the below table.

Bit pattern value
$111$ 3
$110$ 2
$101$ 1
$100$ 0
$011$ $−1$
$101$ $−2$
$001$ $−3$
$000$ $−4$

When the given value is positive, the bit assigned on high order bit is 0 and when the given value is negative, the bit assigned on higher bit is 1.

The best approximation of $110$ is $18$ as $110$ cannot be expressed in binary representation accurately

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Chapter 1, Problem 39CRP

Chapter 1, Problem 41CRP

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Chapter 1 Solutions

Computer Science: An Overview (13th Edition) (What's New in Computer Science)

Ch. 1.1 - What input bit patterns will cause the following...Ch. 1.1 - In the text, we claimed that placing a 1 on the...Ch. 1.1 - Assuming that both inputs to the flip-flop in...Ch. 1.1 - a. If the output of an AND gate is passed through...Ch. 1.1 - Prob. 5QE Ch. 1.1 - Prob. 6QE Ch. 1.2 - If the memory cell whose address is 5 contains the...Ch. 1.2 - Prob. 2QE Ch. 1.2 - Design a sequence of steps that correctly...Ch. 1.2 - How many bits would be in the memory of a computer...

Ch. 1.3 - Prob. 1QE Ch. 1.3 - Prob. 2QE Ch. 1.3 - Prob. 3QE Ch. 1.3 - Prob. 4QE Ch. 1.3 - Prob. 5QE Ch. 1.3 - Prob. 6QE Ch. 1.4 - Here is a message encoded in ASCII using 8 bits...Ch. 1.4 - In the ASCII code, what is the relationship...Ch. 1.4 - Prob. 3QE Ch. 1.4 - Prob. 4QE Ch. 1.4 - Convert each of the following binary...Ch. 1.4 - Prob. 6QE Ch. 1.4 - What is the largest numeric value that could be...Ch. 1.4 - An alternative to hexadecimal notation for...Ch. 1.4 - What is an advantage of representing images via...Ch. 1.4 - Prob. 10QE Ch. 1.5 - Convert each of the following binary...Ch. 1.5 - Convert each of the following base ten...Ch. 1.5 - Convert each of the following binary...Ch. 1.5 - Express the following values in binary notation:...Ch. 1.5 - Perform the following additions in binary...Ch. 1.6 - Convert each of the following twos complement...Ch. 1.6 - Prob. 2QE Ch. 1.6 - Suppose the following bit patterns represent...Ch. 1.6 - Suppose a machine stores numbers in twos...Ch. 1.6 - In the following problems, each bit pattern...Ch. 1.6 - Prob. 6QE Ch. 1.6 - Prob. 7QE Ch. 1.6 - Prob. 8QE Ch. 1.6 - Prob. 9QE Ch. 1.6 - Prob. 10QE Ch. 1.6 - Prob. 11QE Ch. 1.7 - Prob. 1QE Ch. 1.7 - Prob. 3QE Ch. 1.7 - Prob. 4QE Ch. 1.8 - What makes Python an interpreted programming...Ch. 1.8 - Write Python statements that print the following:...Ch. 1.8 - Write Python statements to make the following...Ch. 1.8 - Write a Python statement that given an existing...Ch. 1.9 - Prob. 1QE Ch. 1.9 - Prob. 2QE Ch. 1.9 - Prob. 3QE Ch. 1.9 - Prob. 4QE Ch. 1.9 - Prob. 5QE Ch. 1.9 - Prob. 6QE Ch. 1.9 - Prob. 7QE Ch. 1.10 - Prob. 1QE Ch. 1.10 - Could errors have occurred in a byte from Question...Ch. 1.10 - Prob. 3QE Ch. 1.10 - Prob. 4QE Ch. 1.10 - Prob. 5QE Ch. 1.10 - Prob. 6QE Ch. 1 - Determine the output of each of the following...Ch. 1 - a. What Boolean operation does the circuit...Ch. 1 - a. If we were to purchase a flip-flop circuit from...Ch. 1 - Assume that both of the inputs in the following...Ch. 1 - The following table represents the addresses and...Ch. 1 - How many cells can be in a computers main memory...Ch. 1 - Prob. 7CRP Ch. 1 - Prob. 8CRP Ch. 1 - Prob. 9CRP Ch. 1 - Prob. 10CRP Ch. 1 - Suppose a picture is represented on a display...Ch. 1 - Prob. 12CRP Ch. 1 - Prob. 13CRP Ch. 1 - If each sector on a magnetic disk contains 1024...Ch. 1 - How many bytes of storage space would be required...Ch. 1 - Prob. 16CRP Ch. 1 - Prob. 17CRP Ch. 1 - Suppose a typist could type 60 words per minute...Ch. 1 - Prob. 19CRP Ch. 1 - Prob. 20CRP Ch. 1 - Prob. 21CRP Ch. 1 - Prob. 22CRP Ch. 1 - Prob. 23CRP Ch. 1 - Prob. 24CRP Ch. 1 - Prob. 25CRP Ch. 1 - Prob. 26CRP Ch. 1 - Prob. 27CRP Ch. 1 - Prob. 28CRP Ch. 1 - Prob. 29CRP Ch. 1 - Prob. 30CRP Ch. 1 - Prob. 31CRP Ch. 1 - Prob. 32CRP Ch. 1 - Prob. 33CRP Ch. 1 - Prob. 34CRP Ch. 1 - Prob. 35CRP Ch. 1 - Prob. 36CRP Ch. 1 - Prob. 37CRP Ch. 1 - Prob. 38CRP Ch. 1 - Prob. 39CRP Ch. 1 - Prob. 40CRP Ch. 1 - Prob. 41CRP Ch. 1 - Prob. 42CRP Ch. 1 - Prob. 43CRP Ch. 1 - Prob. 44CRP Ch. 1 - Prob. 45CRP Ch. 1 - What would be the hexadecimal representation of...Ch. 1 - Prob. 47CRP Ch. 1 - Prob. 48CRP Ch. 1 - Prob. 49CRP Ch. 1 - Prob. 50CRP Ch. 1 - Prob. 51CRP Ch. 1 - Prob. 52CRP Ch. 1 - Prob. 53CRP Ch. 1 - Prob. 54CRP Ch. 1 - Prob. 55CRP Ch. 1 - Prob. 56CRP Ch. 1 - Prob. 57CRP Ch. 1 - Prob. 58CRP Ch. 1 - Write and test a Python script that, given a...Ch. 1 - Prob. 61CRP Ch. 1 - Prob. 2SI Ch. 1 - Prob. 3SI Ch. 1 - Prob. 4SI Ch. 1 - Prob. 5SI Ch. 1 - Prob. 6SI Ch. 1 - Prob. 7SI

Knowledge Booster

Bit pattern	value
$111$	3
$110$	2
$101$	1
$100$	0
$011$	$−1$
$101$	$−2$
$001$	$−3$
$000$	$−4$