Binary Representation

Question 1

Bit

Answer 1

Bit: “Binary digiT,” a basic unit of information in a computer
○ 1 bit = a bit
○ 4 bits = a nibble
○ 8 bits = a byte

Question 2

Digital

Answer 2

finite number of symbols (opposite is “analog” i.e. continuous)

Question 3

Signed Magnitude

Answer 3

MSB tells sign of number. No further adjustments
001 = 1
101 = -1
Issue:
- two numbers for 0
- arithmetic not straight forward. Does not work.

Question 4

1C

Answer 4

Flip all digits, to obtain negative of unsigned number
001 = 1
110 = -1

issue:

• two numbers for 0
• Hardware to perform addition is tricky to implement

Question 5

2C

Answer 5

1C + 1 to obtain negative of unsigned number.
Alternative approach: copy bits from right to left up to and including the first “1” and flip remaining bits
Advantage:
- only one representation for zero
- computer can add positive and negative numbers together

Question 6

Floating Point

Answer 6

○ sign, fraction, and exponent
○ N = (-1) S × 1.fraction × 2^(exponent-127)
1__10000001__10101000000000000000000
S__Exponent__Fraction

Question 7

Unsigned overflow

Answer 7

Operation results goes beyond the width of memory location in a computer/ width of machine

Question 8

Signed overflow

Answer 8

positive + positive number -> negative

negative + negative number -> positive

Question 9

ASCII - Size

Answer 9

2^7 = 128 combinations

Question 10

UNICODE - Size

Answer 10

2^32 combinations

Question 11

How do calculations with fractions in binary work

Answer 11

2C addtion and stubtraction still work. To do this, allign binary points

Question 12

Word

Answer 12

bits computer can process in one operation

Question 13

Multiplication of two n bit numbers. Result how many bits

Answer 13

2n

Question 14

Addition of two n bit numbers. Result how many bits

Answer 14

up to n+1

Question 15

Largest and smallest number that can be represented with n bits in 2C

Answer 15

Largest: 2^(n-1)-1
Smallest:-2^(n-1)

Question 16

Sign Extension

Answer 16

Used when adding number of different length
Extend MSB of shorter number for 2C
Extend with 0 in case of unsigned numbers

Question 17

Encoding

Answer 17

Agreed upon ‘mapping’ of data from one representation to another
Examples: ASCII, UNICODE

Question 18

Hexadecimal

Answer 18

fewer digits. More compact and convenient than binary

Just a notation, not a different machine representation

Question 19

Why do we use bias ‘127’ in floating point standard

Answer 19

• Allows us to have a very big range for the exponent from (-127 to 128)
• allows us to represent very big an very small numbers w/o using 2c for the exponent
• Allows us to speed up comparison of floating point numbers. –> Exponent is a 8 bit UNSIGNED number. Easier to compare then if we would need to convert in 2C. The “larger” the exponent number the bigger the number, negatively or positively depending on the Sign.

Question 20

Special Cases IEEE Floating point number

Answer 20

Number 0: Sign = X, Exponent = 0, Fraction =0
Number +Infinity: Sign = 0, Exponent = 11111111, Fraction =0
Number -Infinity: Sign = 1, Exponent = 11111111, Fraction =0
Number NaN: Sign = X, Exponent = 11111111, Fraction =Not Zero
Number: -1^s x 0.fraction x 2^(-126) . Case if exponent = 0 and fraction = not zero

Question 21

How many two input logic functions are possible?

Answer 21

4 input combinations. For every input combination I can assign 0 or 1 as output. i.e. 2^4 = 16