SLR11 - Number Bases

Question 1

How is a number’s base shown using subscript?

Answer 1

Unsigned binary only represents positive numbers. Smallest value = 0, largest = 2ⁿ - 1

Question 2

What is signed binary?

Answer 2

Signed binary uses the MSB as a sign bit:

0 = positive

1 = negative
Used with two’s complement.

Question 3

What is the maximum value you can store in 8-bit unsigned binary?

Answer 3

255 (from 0 to 255)

Question 4

Why is the max value in 8-bit unsigned binary 255 and not 256?

Answer 4

Because we start counting from 0. So 256 values, but highest number is 255.

Question 5

In two’s complement, what is the range for 8 bits?

Answer 5

-128 to +127

Question 6

Why does two’s complement allow one more negative number than positive?

Answer 6

Because the MSB has negative weight (e.g., -128 in 8 bits), and there’s no +128.

Question 7

How do you convert a positive denary to binary?

Answer 7

Divide by 2, record remainders, reverse the result.

Question 8

How do you convert negative denary to binary (two’s complement)?

Answer 8

1. Convert absolute value to binary
2. Invert the bits
3. Add 1

Question 9

How do you convert binary (two’s complement) to denary?

Answer 9

If MSB is 0 → convert normally

If MSB is 1 →
1. Invert the bits
2. Add 1
3. Convert to denary and add minus sign

Question 10

What are the binary addition rules?

Answer 10

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 (carry 1)
1 + 1 + 1 = 1 (carry 1)

Question 11

What are the two possible errors in binary arithmetic?

Answer 11

Overflow: result is too big for available bits

Underflow: result is too small to be stored

Question 12

How do you detect overflow in binary addition?

Answer 12

If carry out of MSB ≠ carry into MSB

Question 13

What is fixed point binary representation?

Answer 13

Binary numbers where the binary point is in a fixed position (e.g., 4 bits for integer, 4 for fraction).

Question 14

Can fixed point binary represent negatives?

Answer 14

Yes, using two’s complement for the integer part.

Question 15

What are limitations of fixed point?

Answer 15

1. Limited range
2. Limited precision
3. Some fractions like 1/3 can’t be stored accurately

Question 16

What is floating point binary representation?

Answer 16

A way to represent real numbers using two parts:

Mantissa = actual digits

Exponent = moves the binary point left/right

Question 17

What is the benefit of floating point over fixed point?

Answer 17

Much wider range, useful for scientific or very large/small numbers.

Question 18

What does a positive exponent mean in floating point?

Answer 18

Move binary point right → larger number

Question 19

What does a negative exponent mean in floating point?

Answer 19

Move binary point left → smaller number

Question 20

In floating point, what does accuracy depend on?

Answer 20

Length of the mantissa

Question 21

In floating point, what does range depend on?

Answer 21

Length of the exponent

Question 22

What is absolute error?

Answer 22

Actual value - stored value

Question 23

What is relative error?

Answer 23

(Absolute error ÷ Actual value) × 100

Question 24

What is hexadecimal?

Answer 24

Base-16 number system. Digits go from 0–9 then A–F.

Question 25

Why is hexadecimal used?

Answer 25

Easier to read than long binary Compact way to represent binary values

Question 26

How many bits does each hex digit represent?

Answer 26

4 bits per hex digit

Question 27

How do you convert binary to hex?

Answer 27

Split into 4-bit chunks, convert each to hex

Question 28

How do you convert hex to binary?

Answer 28

Convert each hex digit to its 4-bit binary equivalent

Question 29

How do you convert hex to denary?

Answer 29

Multiply each digit by its positional value (16ⁿ) and add