CH5

Question 1

Name the four number systems commonly used in programming:
(name with its base)

Answer 1

1. binary (base: 2)
2. octal (base: 8)
3. decimal (base: 10)
4. hexadecimal (base: 16)

Question 2

which number system includes letters?

Answer 2

hexadecimal

Question 3

in the decimal number system, the digits range from?

Answer 3

0 to 9

Question 4

the smallest “unit” of data on a binary computer is a ______ bit.

Answer 4

single

Question 5

T/F: modern computers operate using hexadecimal logic.

Answer 5

F, binary logic.

Question 6

the computer represents values using two voltage levels (usually __V for logic 0 and either ____V or ___V for logic 1).

Answer 6

0V for logic 0, and either +3.3V or +5V for logic 1.

Question 7

Steps for converting from any number system to the decimal number system:

Answer 7

1- number the digits starting from 0. (right to left)
2- multiply each digit to the base of its number system (to the power of the digit’s position)
3- add them all together

[note if the number you are trying to convert has a decimal then every digit before the decimal will have a negative position number (-1, -2,..)]

Question 8

steps of converting from the decimal number system to any other system:

Answer 8

1- divide the number by the base of the system you want to convert it to
2- divide the integer part by the base (until you can’t) and write down its remainder each time.
2- concate each remainder (down to up).

Question 9

In the hexadecimal number system, the letter range from?

Answer 9

from A to F

Question 10

steps converting from binary to any other system:

Answer 10

1- divide the digits into groups of (three[for oct.]/four[for hex.])
2- translate each group .

Question 11

in binary, 1+1 =

Answer 11

10 ( one and zero. not ten. )

Question 12

in binary, 0 - 1 =

Answer 12

take from the neighbouring digit (like normally in subtraction), then the 0 will be 2. so it’ll be 2 - 1 = 1

Question 13

A =

Answer 13

10

Question 14

B =

Answer 14

11

Question 15

C =

Answer 15

12

Question 16

D =

Answer 16

13

Question 17

E =

Answer 17

14

Question 18

F =

Answer 18

15

Question 19

Remember that when converting a hexadecimal to a decimal the letter will be switched to a number and taken as a whole.

Answer 19

example: (AF)16
A = 10, F = 15
(10 x 16 to the power of 1) + (15 x 16 to the power of 0)

Question 20

A(A’) =

Answer 20

0

Question 21

A + (A’) =

Answer 21

1

Question 22

In Boolean algebra, 1 is considered

Answer 22

true (T)

Question 23

In Boolean algebra, 0 is considered

Answer 23

false (F)

Question 24

a + 0 =

Answer 24

a

Question 25

A (1) =

Answer 25

A

Question 26

(AB)' =

Answer 26

A' OR B'

Question 27

(A + B)' =

Answer 27

(A')(B')

Question 28

________ describes operations on true/false values.

Answer 28

boolean algebra

Question 29

Boolean logic operations on electronic signals can be build out of _______ and other electronic devices.

Answer 29

transistors

Question 30

signals are the

Answer 30

boolean variables.

Question 31

circuits are the

Answer 31

boolean functions.

Question 32

are hardware devices built from transistors to mimic Boolean Operations

Answer 32

gates

Question 33

is a collection of logic gates

Answer 33

circuit

Question 34

T/F: Signals transform a set of binary inputs into a set of binary outputs

Answer 34

F, Circuts.

Question 35

CE circuit

Answer 35

Compare-for-equality (CE) circuit

Question 36

_____ compares two unsigned binary integers for equality.

Answer 36

CE

Question 37

CE Circuit is built by combining together _____-bit comparison circuits (___-CE)

Answer 37

1-bit (1-CE)

Question 38

CE (F) =

Answer 38

F = A'B' + AB = 1 + 1 which is (0)(0) + (1)(1)

Question 39

(x'y')' =

Answer 39

x + y

Question 40

In __________, both circuits produce the exact same output for each input value combination

Answer 40

circuit equivalence

Question 41

Boolean algebra allows us to apply provable mathematical principles to help us find simpler design for the logical circuits. This is called:

Answer 41

minimization