Part 1 Block 1 - Binary

Question 1

As we know, binary consists of ‘0’s and ‘1’s.
0, when the electricity is off, and 1 when it is on.
It is not quite as simple as this.
What is the range of volts for ‘0’ or off?
What is the range of volts for ‘1’ or on?

Answer 1

0 - 1.3v for ‘0’s
1.7+ for ‘1’s

Question 2

Why is there a gap between 1.3v and 1.7v?

Answer 2

This gap means that if there is any small random dips or increases in the voltage (called noise), the two binary digits will still be distinguishable.

Question 3

If the level of noise is too high, there is a small chance that the voltage might be pushed into the gap or even into the wrong range.
What is this called?

Answer 3

A bit error

Question 4

If bit errors can occur, why not raise the voltage of the ‘1’s to widen the gap?

Answer 4

More voltage, more heat, more problems!

Question 5

The process of combining the symbols (e.g. ‘0’s and ‘1’s) to represent data is called _____________?

Answer 5

encoding

Question 6

If two or more number systems are being considered, we use a ______________ to show which representation is being used.

Answer 6

subscript

e.g. 1001 = 9
2 10

Question 7

When we consider binary representations in the context of computing, we often talk about each symbol being stored in a bit. So how many bits would the binary number 1001 be?

Answer 7

4 bits long

Question 8

Covert the denary number 53 into an 8-bit binary number.

Answer 8

0011 0101

Question 9

When we write long binary numbers we divide them into groups of ____?

Answer 9

4

e.g. 00110101 becomes 0011 0101

Question 10

An unsigned integer is an integer that is …?

Answer 10

Greater than or equal to zero and only ever positive.

Question 11

What denary numbers could we represent with 3-bits (aka 2^3)

Answer 11

2^3 = 8
So, we can represent 8 denary numbers, 0-7

e.g. 000 = 0
001 = 1
010 = 2

Question 12

What is the result of the following addition in binary?
110 + 101 =

What happens to the number of bits?

Answer 12

= 1011

The number of nits increases from 3-bits to 4-bits.

Question 13

Can we represent negative numbers in binary?

Answer 13

Yes, we can.

Question 14

How can we represent a negative denary number with a 3-bit binary number and what is it called?

Answer 14

We can use the first bit to represent either a positive or a negative.
e.g. a zero could rep a positive and a 1could rep a negative:

001 = 1
101 = -1

This representation is called:
sign-magnitude representation

Question 15

If we have 4 bits, which means 2^4, so 16 different integers that can be encoded, how many can be used to represent negatives?

Answer 15

As we know, the rule in sign magnitude representation is that if we have n bits available, there will be 2^n possible encodings.

Half of them, so 2^n/2, will be used to represent 0 and positive integers, and half of them will be used to -0 and the other negative integers.

Question 16

Regarding positive and negative numbers in the sign-magnitude representation, the formula for how many numbers can be positive or negative is 2^n/2-1.

What is the largest positive binary number that can be written in 4 bits in the sign-magnitude representation?

Answer 16

7

Question 17

What is the drawback of sign-magnitude representation?

Answer 17

There are two representations of 0.
+0 and -0

Question 18

Find the sum of the following sign-magnitude numbers:

0010 + 1111

Answer 18

(0010 is positive and 1111 is negative)

1101 (remember, the first 1 stands for
the negative sign)

Question 19

Is there a negative zero in the two’s complement representation of binary?

Answer 19

No

Question 20

In the two’s complement representation of binary, what happens to the block of negative numbers?

Answer 20

We shift them to the left.

Question 21

Are there still as many binary encodings available in the Two’s Complement Representation?

Answer 21

Yes, it is still 2^n

Question 22

Are there still 2^n/2 encodings available for both the positives and the negatives?

Answer 22

Yep!

Question 23

What is the largest positive integer that can be represented in n-bit two’s complement?

What is the negative integer with the largest magnitude that can be written in n-bit two’s complement.

Answer 23

2^n/2 - 1

-2^n/2

Question 24

Two’s Complement Representation

What is the largest positive decimal integer that can be written in 8-bit two’s complement representation?

Answer 24

127

Question 25

Two’s Complement Representation

What is the 8-bit two’s complement binary encoding of the largest positive decimal integer?

Answer 25

0111 1111

Question 26

Two’s Complement Representation

What is the negative decimal integer with the largest magnitude that can be written in an 8-bit two’s complement representation?

Answer 26

–128

Question 27

Two’s Complement Representation

What is the 8-bit binary encoding of the negative decimal integer with the largest magnitude?

Answer 27

1000 0000

Question 28

Two’s Complement Representation

What is the two’s complement encoding of 0 in 8-bit two’s complement representation?

Answer 28

0000 0000

Question 29

Complete the following addition problems in two’s complement.

a.4 + (–1)
b.–5 + 2
c.–4 + (–3)

Answer 29

a) 0011

b) 1101

c) 1001

Question 30

What is UTF-8?

Answer 30

the standard encoding system for characters - Unicode Transformation Format-8
It uses a variable number of bytes (up to 6) to encode characters in use across the world.