Express − 7 2 using the 8-bit floating point format. The process to encode the values using the 8-bit floating point format is, 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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1. Convert the number − 7 into binary equivalent. 2 7 2 3 1 2 1 1 0 1 The binary representation is the sequence of the remainder from down to bottom

Question

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Answer 1

Expert Solution & Answer

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Expert Solution & Answer

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Check out a sample textbook solution

See solution

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Answer 2

Expert Solution & Answer

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Answer 8

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

Answer 9

Chapter 1, Problem 37CRP

a.

Explanation of Solution

Express −72 using the 8-bit floating point format.

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number −7 into binary equivalent.

2723121101

The binary representation is the sequence of the remainder from down to bottom

Answer 10

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

Answer 11

b.

Explanation of Solution

Express 12 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 12 into binary representation

Answer 12

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

Answer 13

c.

Explanation of Solution

Express −334 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3 into binary equivalent.

2321101

The binary representation is the sequence of the remainder from down to bottom.

(3)10=(11)2

Convert the number 34 into binary representation

Answer 14

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

Answer 15

d.

Explanation of Solution

Express 732 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 732 into binary representation

Answer 16

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Answer 17

e.

Explanation of Solution

Express 3132 using the 8-bit floating point format:

The process to encode the values using the 8-bit floating point format is,

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 imagine the pattern of mantissa field with a radix at its left and obtain 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 then the bit assigned on high order bit is 0 and when the given value is negative then the bit assigned on higher bit is 1.

Convert the number 3132 into binary representation.

732=1×12+1×14+1×18+1×116+1×132</

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

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...

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

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

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Chapter 1 Solutions