Chapter 1, Problem 36CRP

a.

Explanation of Solution

Decode $01011001$ using the floating point format described in figure 1.24:

The rules of the floating format is,

• The high order bit of the binary number is the sign bit. 0 is assigned as positive and 1 is assigned as negative.
• The four bits from the right are assigned as mantissa field.
• 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
$011$	$-1$
$101$	$-2$
$001$	$-3$
$000$	$-4$

• Apply the above rules to the bit pattern $01011001$.
• The mantissa field of the given binary number is $.1001$, shift 1 bit to the left of the decimal point then the exponential field $001$ represents 1 by follow the above table.. the number becomes $1.001$
• Convert the number 1 into base ten representation

b.

Explanation of Solution

Decode $11001000$ using the floating point format described in figure 1.24:

The rules of the floating format is,

• The high order bit of the binary number is the sign bit. 0 is assigned as positive and 1 is assigned as negative.
• The four bits from the right are assigned as mantissa field.
• 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
$011$	$-1$
$101$	$-2$
$001$	$-3$
$000$	$-4$

• Apply the above rules to the bit pattern $11001000$.
• The mantissa field of the given binary number is $.1000$, shift 1 bit to the left of the decimal point then the exponential field is $100$ represents 0 by follow the above table.. then there is no need to shift the bit number and the number becomes $0$

c.

Explanation of Solution

Decode $10101100$ using the floating point format described in figure 1.24:

The rules of the floating format is,

• The high order bit of the binary number is the sign bit. 0 is assigned as positive and 1 is assigned as negative.
• The four bits from the right are assigned as mantissa field.
• 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
$011$	$-1$
$101$	$-2$
$001$	$-3$
$000$	$-4$

• Apply the above rules to the bit pattern $10101100$.
• The mantissa field of the given binary number is $.1100$, shift 2 bit to the left of the decimal point then the exponential field $010$ represents $-2$  by follow the above table. The number becomes $0.001100$
• Convert the number $0.001100$ into binary representation.

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d.

Explanation of Solution

Decode $00111001$ using the floating point format described in figure 1.24:

The rules of the floating format is,

• The high order bit of the binary number is the sign bit. 0 is assigned as positive and 1 is assigned as negative.
• The four bits from the right are assigned as mantissa field.
• 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
$011$	$-1$
$101$	$-2$
$001$	$-3$
$000$	$-4$

• Apply the above rules to the bit pattern $00111001$.
• The mantissa field of the given binary number is $.1001$, shift 1 to the left of the decimal point then the exponential field $011$ represents $-1$  by follow the above table. then  number becomes $0.01001$
• Convert the number $0$