105

Question 1

What is the decimal number system?

Answer 1

> Base 10 system

> Maximum number value that can be stored goes up by the equation 10^n - 1

Question 2

What is the binary number system?

Answer 2

> Base 2 system

> The max value that can be stored goes up by the equation 2^n - 1

Question 3

How are binary numbers grouped?

Answer 3

> In groups of 4

> Leading 0’s are added

Question 4

What is a 4 bit group called?

Answer 4

A nibble

Question 5

What is an 8 bit group called?

Answer 5

Byte

Question 6

What is the hexadecimal number system?

Answer 6

> Base 16 system
Symbols 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
A-F represents 10-15
The max number that can be stored goes by the equation: 16^n - 1

Question 7

Why is hexadecimal useful when compared to binary?

Answer 7

Each nibble can be represented by a single hexadecimal digit

Question 8

How are hexadecimal often notated?

Answer 8

> This a 0x at the front

Question 9

How are decimal numbers converted to binary?

Answer 9

> Construct the decimal number by summing powers of 2

> 97 = (2^6) + (2^5) + (2^0)

Question 10

How are binary numbers converted to hexadecimal?

Answer 10

Split the binary number into nibbles and convert each nibble into a corresponding hexadecimal number

Question 11

How are hexadecimal numbers converted to binary?

Answer 11

Convert each hexadecimal digit into the equivalent nibble

Question 12

How are decimal number converted to hexadecimal?

Answer 12

> Construct the decimal number by summing multiples of powers of 16
> 3740 = 14(16^2) + 9(2^1) + 12(2^0) = 0xE9C
# 3740/16^2 = 14 remainder 156
# 156/16^1 = 9 remainder 12
# 12/16^0 = 12
# so 0xE9C

Question 13

What is a signed number?

Answer 13

> A way of writing negative numbers in binary
Positive integers are unsigned integers
Negative integers are signed integers

Question 14

What are the 3 ways of displaying negative numbers?

Answer 14

> Sign-magnitude format
1’s Complement format
2’s Complement format

Question 15

What is sign-magnitude format?

Answer 15

> Most significant bit is used to represent the sign
0 represents positive numbers
1 represents negative numbers
The remaining bits represent the number

Question 16

What is the problem with sign-magnitude format?

Answer 16

> There are 2 ways of representing 0
0000
1000

Question 17

What is the range of sign-magnitude format?

Answer 17

-2^(n-1) + 1 ≤ x ≤ 2^(n-1) - 1

Question 18

What is 1’s compliment?

Answer 18

> Positive numbers are represented normally

> Negative number are represented as the inverse (1’s become 0 and 0’s become 1)

Question 19

What is the problem with 1’s complement?

Answer 19

> There are 2 ways of representing 0
0000
1111

Question 20

What is 2’s complement?

Answer 20

> This is a method of representing positive and negative numbers without there being 2 numbers for 0

Question 21

What is the range of 1’s complement?

Answer 21

-2^(n-1) + 1 ≤ x ≤ 2^(n-1) - 1

> Same as sign-change

Question 22

How does 2’s complement work?

Answer 22

> The most significant bit is treated as negative and the rest is calculated like normal.

Question 23

What are the parallels between 1’s and 2’s complement?

Answer 23

> 2’s Complement is the same as 1’s Complement except 1 has been added to the number

Question 24

What is the range of 2’s complement?

Answer 24

> It is 1 decimal number larger than 1’s complement because there is only one representation of 0 (0000)
-2^(n-1) ≤ x ≤ 2^(n-1) - 1

Question 25

What are the 4 basic rules for adder circuits?

Answer 25

> 0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 carry 1 = 10

Question 26

What is a half adder? What is the circuit?

Answer 26

> This is a circuit that sums 2 bits
An XOR gate for the sum bit in parallel with…
An AND gate for the carry bit

Question 27

What happens when you have multiple bits to be added in a half adder system?

Answer 27

The carry bit is then fed into the next adder which has 3 input gates

Question 28

What is a full adder?

Answer 28

> This takes into consideration the carry bit into the addition of 2 bits.
Multiple full adders can be strung together to add multiple bits

Question 29

What are the 2 boolean expressions for a full adder?

Answer 29

> sum= A⨁B⨁Ci

> Co=A.B+Ci.(A⨁B)

Question 30

What is it called when multiple full adders are joined together?

Answer 30

A ripple adder

Question 31

Do ripple adders work for all signed numbers?

Answer 31

> No

> Just 2’s complement

Question 32

How can a ripple adder work with 2’s complement?

Answer 32

As long as the final carry bit is ignored