lecture 6

Question 1

machine language

Answer 1

binary numbers only

Question 2

binary encoding

Answer 2

convert data into different form or representation

Question 3

base-10

Answer 3

decimal numbers
0-9

Question 4

base-2

Answer 4

binary
0-1

Question 5

base-16

Answer 5

hexidecimal
0-9, A-F

Question 6

base-10 equation

Answer 6

v = Σ (10^i)(d)
*key:
v –> base-10 value
i –> digit position (increases right
to left starting @ 0)
d –> decimal digit

Question 7

what is each base-10 digit multiplied by?

Answer 7

power of 10

Question 8

base-10 example)
173
1 7 3

= 173
how is this equal to 173?

Answer 8

1 7 3
10^2 + 10^1 + 10^0
= 1(10^2) + 7(10^1) + 3(10^0)
= 173

Question 9

base-2 equation

Answer 9

v = Σ 2^i bi
*key:
v –> base-2 number
i –> digit position (increasing
from right to left, starting @
0)
b –> binary digit (either 1 or 0)

Question 10

what is each base-2 digit multiplied by?

Answer 10

power of 2

Question 11

base-2 example)
011111010000

= 2000 (base-10)
how is this equal to 2000?

Answer 11

0 1 0 0 1 0 0 1
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

= 1(2^6) + 1(2^3) + 1(2^0)
= 64 +8 +1
= 73

Question 12

what is the most significant bit?

Answer 12

msb –> always going to be the greatest power of 2
(right most bit)

Question 13

what is the least significant bit?

Answer 13

lsb –> always going to be the lowest power of 2
(left most bit)

Question 14

0 1 0 0 1 0 0 1
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

what is the msb?

Answer 14

2^7
- greatest power of 2 (right most bit)

Question 15

0 1 0 0 1 0 0 1
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0

what is the lsb?

Answer 15

2^0
- least power of 2 (left most bit)
**always going to be 2^0

Question 16

decimal to binary algorithm

Answer 16

v/2 = quotient, remainder = bit (going to be 0 or 1)
quotient/2, remainder = next bit (going to be 0 or 1)
STEPS:
divide v by 2
remainder becomes next bit
quotient becomes next v
**repeat until v = 0
- msb –> last bit found when v
= 0
- lsb –> first bit found
* first division –> remainder = lsb
* last division –> remainder = msb

Question 17

base-16 equation

Answer 17

v = Σ 16^i d
*key:
v –> base-10 value
i –> digit position (increasing from
right to left, starting @ 0)
d –> hexit

Question 18

base-16 0-9 chart

Answer 18

0 - 0
1 - 1
2 - 2
3 - 3
4 - 4
5 - 5
6 - 6
7 - 7
8 - 8
9 - 9

Question 19

base-16 A-F chart

Answer 19

10 - A
11 - B
12 - C
13 - D
14 - E
15 - F

Question 20

what is each base-16 digit multiplied by?

Answer 20

power of 16

Question 21

how many bits is one hexit digit?

Answer 21

4 bits

Question 22

if you are converting binary to hexit, how do you go about doing this?

Answer 22

break up the binary digits every 4 digits starting at the lsb (leftmost bit)
- in each of these segments, the
digits’ indexes are from 2^0 to
2^3
- do the usual calculation and that’s
the hexit representation

Question 23

binary to hexit example)
011111010000

= 0x7D
how does this work?

Answer 23

011111010000
A) break up the binary into groups of 4
0111 1101 0000
B) calculate what number each 4 digits add up to
0000 = 0
1 1 0 1
2^3. 2^2. 2^1. 2^0
= 8 + 4 + 1
= 13 –> D
0 1 1 1
2^3. 2^2. 2^1. 2^0
= 4 + 2 + 1
= 7
C) put it together
011111010000 = 0x7D

Question 24

ASCII encoding allows what

Answer 24

conversion from character to number

Question 25

what is signed magnitude representation?

Answer 25

used to encode positive and negative binary numbers

Question 26

are the positive and negative binary representations different in signed magnitude?

Answer 26

no

Question 27

what is the difference between positive and negative binary reps in signed mag?

Answer 27

msb (most significant bit)
- msb = 0, positive number
- msb = 1, negative number

Question 28

range for values able to be represented in signed magnitude rep

Answer 28

-(2^N-1 - 1) to (2^N-1 - 1)

N = # of bits

Question 29

pros of signed magnitude

Answer 29

easy to negate
easy to compute abs value

Question 30

cons of signed magnitude

Answer 30

add/subtract is complex
2 different ways of repping 0
+0 and -0 –> two different things

Question 31

what is signed magnitude used for?

Answer 31

floating point representation
**not integers

Question 32

what is the two-step process for 2’s complement?

Answer 32

1. complement every bit
   - 1 –> 0, 0 –> 1
2. add 1 (binary addition)

** if neg –> pos rep
**if pos –> neg rep

Question 33

range for 2’s complement

Answer 33

(-2^N-1) to (2^N-1 -1)

N = # of bits

Question 34

is 2’s complement the same process for negating a negative binary number?

Answer 34

yes

Question 35

is adding the same thing as subtracting in 2s complement?

Answer 35

yes

Question 36

what is sign extension?

Answer 36

when you pad the binary number with 0s or 1s (to preserve the sign) if you need it to be an “extended”/bigger amount of bits

Question 37

pros of 2s complement

Answer 37

only add operation
only one zero rep
sign extension

Question 38

cons of 2s complement

Answer 38

more complex to negate and compute abs value

Question 39

floating point rep

Answer 39

(sign) (significand) x 2^(exponent)

• sign –> positive and negative number determinant
• normalized fraction (significand)
• exponent (position of the “floating” binary point)

Question 40

what is IEEE 754 floating point rep?

Answer 40

used to represent double/float numbers (fractions)
sign field (s) –> 1 bit
- 0 : pos, 1 : neg
exponent field (E)
- 8 bits (exponent + 127)
fraction field –> 23 bits
- 23 bits significand w/o leading 1
*1 –> hidden (normalized)

Question 41

IEEE 754 floating point rep steps

Answer 41

1. convert to binary
   - 4 bits on either side of decimal place
2. normalize the fraction to 1.F
   - move it until its 1.F
3. calculate the exponent
   - based on how many places you moved to normalized –> E - 127
   - convert to binary