Deck 6: Digital Arithmetic: Operations and Circuits

Question 1

What is the minimum number of bits required to represent - 143₁₀ as a signed binary number in 2's- complement form?

A) 8
B) 7
C) 10
D) 9

Answer 1

9

Question 2

In using the 2's- complement system of subtraction, a negative number in the subtrahend would ultimately be changed to:

A) a negative number in true binary form.
B) a positive number in true binary form.

Answer 2

a positive number in true binary form.

Question 3

If the numbers 8₁₀ and 9₁₀ are converted to BCD and added, the initial result would be:

A) 0100 1000
B) 1000 0100
C) 0010 0001
D) 0001 0001

Answer 3

0001 0001

Question 4

In the preceding problem, the erroneous answer generated would be corrected by:

A) converting both BCD code groups to straight binary form and subtracting 0110 from the least significant code group.
B) adding 0110 to the least significant code group.
C) adding 0110 to both the most and least significant BCD code groups.
D) adding 0110 to the most significant code group.

Question 5

The following is a 2's- complement signed binary number: 100000000. What is its decimal value?

A) - 255₁₀
B) - 256₁₀
C) - 128₁₀
D) - 0₁₀

Question 6

Which of the following represents the four possible outcomes when adding two binary numbers?

A) 0 + 0 = 0, 1 + 0 = 01, 1 + 1 = 11, 1 + 1 + 1 = 11
B) 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 01, 1 + 1 + 1 = 11
C) 0 + 0 = 1, 1 + 0 = 1, 1 + 1 = 01, 1 + 1 + 1 = 01
D) 0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 10, 1 + 1 + 1 = 11

Question 7

The 5- bit 2's- complement equivalent of 12₁₀ is:

A) 01100
B) 11100
C) 00100
D) 10100

Question 8

The 5- bit 2's- complement of - 12₁₀ is:

A) 10100
B) 01100
C) 00100
D) 11100

Question 9

Multiplication of the unsigned numbers 101101₂ and 1011₂ results in a product of:

A) 101101111₂
B) 111101111₂
C) 110101111₂
D) 111111111₂

Question 10

The MOST commonly used system for representing signed binary numbers is the:

A) sign- magnitude system.
B) 2's- complement system.
C) 10's- complement system.
D) 1's- complement system.

Question 11

When performing subtraction by 2's- complement addition:

A) the minuend is left in its original form and the subtrahend is changed to its 2's- complement.
B) the minuend and subtrahend are both left in their original form.
C) the minuend is changed to 2's- complement and the subtrahend are both changed to the 2's- complement.
D) the minuend and subtrahend are both changed to the 2's- complement.

Question 12

What is the difference between the sign- magnitude and 2's- complement systems of representing signed binary numbers?

A) In the 2's complement system all numbers, regardless of signs, are entered in the2's- complement preceded by a "1" or "0" to denote sign. In the sign- magnitude method, the magnitude bits represent the true binary value and the bit preceding the MSB represents the sign of the following bits.
B) In the signed- magnitude system all numbers, regardless of their sign, are in straight binary format preceded by a "0" or "1" to denote the sign. In the 2's complement system, the negative numbers are entered in the 2's- complement form preceded by a "1" to acknowledge a negative number whereas positive numbers are entered in straight binary format preceded by a "0" to indicate the sign.
C) In the sign- magnitude system all numbers, regardless of their sign, are in the 2's- complement form preceded by a "0" or "1" to indicate their sign. On the other hand, the 2's- complement system requires the sign- magnitude bits be in straight binary format preceded by a "0" or "1" to denote the proper sign.
D) In the 2's- complement system, all positive numbers are entered in the 2's- complement form preceded by "0" to indicate the sign and all negative numbers are entered in straight binary format preceded by a "1" to indicate the sign. The sign- magnitude system requires that positive and negative numbers be entered in straight binary form preceded by a "0" or "1" to indicate the proper sign.

Question 13

One advantage of using the 2's- complement system to represent signed numbers is:

A) addition can be accomplished by performing subtraction.
B) division can be accomplished by performing multiplication.
C) multiplication can be accomplished by performing division.
D) subtraction can be accomplished by performing addition.

Question 14

The 2's- complement method of subtraction is to be performed on the 2's- complement signed numbers = 43(- )- 47. Select the correct minuend, subtrahend, signed binary difference, and decimal result.

A) 00101011 + 11010001 = 11111100 = - 90₁₀
B) 00101011 + 00101111 = 01011010 = - 90₁₀
C) 11010100 + 10101111 = 110000011 = 90₁₀
D) 00101011 + 00101111 = 01011010 = 90₁₀

Question 15

What is the decimal value of the 2's- complement signed binary number 110101101?

A) +l74₁₀
B) +83₁₀
C) - 83₁₀
D) - 174₁₀

Question 16

When multiplying numbers in the 2's- complement system, the product's sign is:

A) negative if the signs of the multiplier and multiplicand are the same.
B) negative if the multiplier and multiplicand are both positive signs.
C) positive if the signs of the multiplier and the multiplicand are the same.
D) positive if the sign bits of the multiplier and multiplicand are opposite.

Question 17

Which of the following represents the 2's- complement of the binary number 100110110101₂?

A) 111001001010
B) 100110110101
C) 011001001011
D) 101100100101

Question 18

The 2's- complement system is to be used to add the signed binary numbers 11110010 and 11110011. Determine the sign and decimal value of each of these numbers and their sum.

A) - 113 and - 114, - 227
B) - 14 and - 13, - 27
C) - 11 and - 16, - 27
D) - 27 and - 13, - 40

Question 19

The 1's- complement of the binary number 010110101₂ is:

A) 011001010
B) 101001000
C) 101001010
D) 101110101

Question 20

A certain register used to store signed binary numbers provides a 16- bit output. Determine the range of register output values and how many different values the register is capable of containing.

A) Range: - 32,768₁₀ to +32,767 Values: 65,536₁₀
B) Range: - 32,768₁₀ to +32,768 Values: 65,535₁₀
C) Range: - 65,536₁₀ to +65,536 Values: 131,071₁₀
D) Range: - 65,536₁₀ to +65,535 Values: 131,072₁₀

Question 21

The 2's- complement method of subtracting +28₁₀ from - 67₁₀ produces a signed binary and decimal difference of:

A) 01011111, +95₁₀
B) 11011111, - 95₁₀
C) 01011111, - 95₁₀
D) 11011111, +95₁₀

Question 22

Which of the following represents the 2's- complement representation for +93₁₀?

A) 00100010
B) 11011101
C) 10100010
D) 01011101

Question 23

The arithmetic overflow in the 2's- complement addition problem of 100001 + 100010 should be:

A) no cause for suspicion because the sign bit often changes during the addition process.
B) disregarded because the sum is small enough to fit in five magnitude bits.
C) disregarded because negative values are being added.
D) a cause for suspicion because the sign bit of the sum does not match the sign of the addend and augend.

Question 24

To correctly represent a positive signed number in 2's- complement form:

A) represent the magnitude in its true binary form and place a sign bit of "1" in front of the MSB.
B) represent the magnitude in its 2's- complement form and place a sign bit of "O" in front of the MSB.
C) represent the magnitude in its 2's- complement form and place a sign bit of "1" in front of the MSB.
D) represent the magnitude in its true binary form and place a sign bit of "O" in front of the MSB.

Question 25

The number - 7₁₀ is to be stored in an 8- bit register as a signed binary number in 2's- complement form. Which of the following represents the register contents?

A) 10000111
B) 01111001
C) 11111001
D) 00000111

Question 26

Which of the following represents the 2's- complement for the signed number - 78₁₀?

A) 00110010
B) 01001110
C) 11001110
D) 10110010

Question 27

4CA5₁₆ + FEA2₁₆ =_____

A) 15C47₁₆
B) 2FB47₁₆
C) 14C47₁₆
D) 14B47₁₆

Question 28

The BCD representation of (275₁₀ + 965₁₀) is_____

A) 0001 0010 0100 0000
B) 1011 1110 1010
C) 0010 0011 0100 0000
D) 1110 1010 1110

Question 29

The carry propagation delay in full- adder circuits:

A) decreases in a direct ratio to the total number of FA stages.
B) is cumulative for each stage and limits the speed at which arithmetic operations are performed.
C) increases in a direct ratio to the total number of FA stages but are not a factor in limiting the speed of arithmetic operations.
D) is normally not a consideration because the delays are usually in the nanosecond range.

Question 30

The BCD representation of (47₁₀ + 83₁₀) is_____

A) 1000 0011
B) 1100 1010
C) 0001 0011 0000
D) 0001 1100 1010

Question 31

The result of any arithmetic operations performed by the ALU is immediately stored in the:

A) memory unit.
B) A register.
C) control unit.
D) B register.

Question 32

How many BCD adders would be required to add the numbers 973₁₀ + 39₁₀?

A) 4
B) 5
C) 6
D) 3

Question 33

The BCD addition of 9₁₀ and 7₁₀ generates code groups of 1001 0111 and a carry to the next higher position. The final step in the problem is to:

A) ignore the lowest order code group because 0000 is a valid code group and prefix the carry with three zeros.
B) disregard the carry and add 0110 to the lowest order code group.
C) add 0110 to the lowest order code group and then prefix the carry with three zeros.
D) add 0110 to both code groups to validate the carry from the lowest order code group.

Question 34

How many inputs must a full- adder have?

A) 5
B) 3
C) 4
D) 2

Question 35

C5₁₆ + AF₁₆ =_____

A) 1A4₁₆
B) 1CF₁₆
C) 174₁₆
D) 14A₁₆

Question 36

The operations of addition and subtraction of signed binary numbers may be accomplished with parallel full- adders, provided that:

A) negative numbers are represented in 2's- complement form and a means is provided to take the 2's- complement of the minuend in subtraction problems.
B) negative numbers are represented in 2's- complement form and a means is provided to take the 2's- complement of the subtrahend in subtraction operations.
C) negative numbers are represented in 2's- complement form and a means is provided for taking the 2's- complement of the minuend and the subtrahend in subtraction problems.
D) positive numbers are represented in 2's- complement form and a means is provided to take the 2's- complement of the minuend in subtraction problems.

Question 37

Which of the following represents the 2's- complement of the hexadecimal number 2AF?

A) D50
B) D51
C) E50
D) E51

Question 38

Assume that you want to design a circuit to multiply to 4- bit unsigned numbers. How many megafunction LPMs would you require?

A) 3
B) 2
C) 4
D) 1

Question 39

The problem (F79₁₆ - BA4₁₆) is performed using 2's- complement arithmetic. Which of the following correctly illustrates the problem?

A) 086 + BA4 = C4A
B) F79 - BA4 = 365
C) F79 + 45C = 3D5
D) 086 + 45C = 5E2

Question 40

How many bits are required to represent 513₁₀ as a signed binary numbers in 2's complement form?

A) 10
B) 8
C) 11
D) 9

Question 41

What is the decimal equivalent of the 2's complement signed number 10110?

A) 8
B) - 5
C) 10
D) - 10

Question 42

Multiplication of the unsigned binary numbers 10010 and 11101 results in a product of:

A) 1110001010
B) 101010101
C) 1000001100
D) 1000011110

Question 43

What is the decimal equivalent of the 2's complement signed number 11011001?

A) 25
B) - 39
C) - 18
D) 29

Question 44

Which of the following is the 2's- complement of the binary number 1001001001001?

A) 10100001
B) 11100111
C) 0100101100
D) 000101011

Question 45

Which of the following is the 2's- complement of the signed decimal number +7525?

A) 1110100000101
B) 1010101010101
C) 0001001111010
D) 1110101100101

Question 46

The number - 9₁₀ is to be stored in an 8- bit register as a signed binary number in 2's- complement form. Which of the following represents the register contents?

A) 11111010
B) 00110101
C) 00011101
D) 10000111

Question 47

Which of the following is the 2's- complement for the signed number - 54₁₀?

A) 1111010
B) 0000101
C) 1001010
D) 0010101

Question 48

CA2₁₆ + BCF₁₆ =_____

A) 1200₁₆
B) 1611₁₆
C) 1871₁₆
D) 1520₁₆

Question 49

The 2's- complement operation on a signed number changes a positive number to a negative number and vice versa.

Question 50

A sign bit of "1" in the result (difference) of a 2's- complement subtraction indicates the magnitude is negative and in true binary form.

Question 51

It is not necessary for the values being added to have the same number of bits when performing 2's- complement addition (or subtraction).

Question 52

A half adder is normally used when a carry input may be applied.

Question 53

In a sign- magnitude format, a "1" in the sign bit position indicates the number is negative.

Question 54

[A] represents "the contents of register A."

Question 55

An overflow indicator in an ALU circuit indicates that the result of an arithmetic operation requires more than four bits.

Question 56

ALU circuits perform arithmetic and logic operations.

Question 57

ALU circuits cannot be cascaded to perform functions on more than four bits.

Question 58

Digital computers add only two binary numbers at a time.

Question 59

Only four possible cases can occur when adding two binary bits.

Question 60

When adding numbers in the 2's complement system, always carry the sign bit.

Question 61

All arithmetic operations take place in the ALU.

Question 62

The ALU contains at least two registers: the A register and the B register.

Question 63

In order to reduce propagation delay in adder circuits it is necessary to build in additional circuitry.

Question 64

The 1's- complement of 1010 is 0101.

Question 65

In sign- magnitude format, a 1 sign bit indicates a negative number.

Question 66

In hex addition, mentally convert values greater than 16, and then add.

Question 67

In BCD addition, the value_____is added to any invalid code group.

Question 68

The solution to 101101.10 - 011101.01 is _____.

Question 69

In sign- magnitude form, a 0 in the sign bit indicates a _____ number.

Question 70

The 2's complement of 13₁₀ is _____ .

Question 71

Subtraction in the 2's complement system actually involves the operation of _____.

Question 72

In the expression 4- 2, 4 is the_____ .

Question 73

In the expression 4- 2, 2 is the _____.

Question 74

The decimal equivalent of the 2's complement signed number 1000 is_____.