1.03 - Internal coding of numbers

Question 1

Define the sign and magnitute representation

Answer 1

It is a signed integer that has a binary code of the value (Magnitude) and an extra bit to define the sign (Sign)

0 is (+) and 1 is (-)

Question 2

Why are signed integers usually in two’s complement form?

Answer 2

Because there are a lot of disadvantages in using signed integers.

Question 3

Define the one’s complement of a binary number

Answer 3

It is defined as the binary number obtained if each binary digit is individually substracted by 1. This means that each 0 is switched to 1 and 1 to 0 (Flip)

Question 4

Define the two’s complement form

Answer 4

It is defined as the binary number obtained if 1 is added to the one’s complement form

Question 5

Explain the quicker method to convert binary to two’s complement form

Answer 5

First, start from the right and move to the left ignoring any 0s up to the first 1 which will also be ignored.
Then flip the remaining bits (0 to 1/ 1 to 0)

Question 6

How to convert (+) denary number to its two complement binary form?

Answer 6

1. Convert denary value to binary
2. Add a 0 infront of this binary value

Question 7

How to convert a (-) denary value into its two’s complement binary form?

Answer 7

1. Disreagard the sign and convert to binary
2. Add 0 infront of this binary value
3. Convert binary value into two’s complement form

Question 8

How to convert a two’s complement binary value into a (+) denary value?

Answer 8

The leading zero is ignored and the remaining is converted to denary

Question 9

How to convert a two’s complement binary value into a (-) denary value?

Answer 9

Convert the binary value into denary the usual way but treat the most significant bit as a negative

Question 10

What are the rules for the addition of binary digits?

Answer 10

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 1 = 0 (carry of 1)
• 1 + 1 + 0 = 0 (carry of 1)
• 1 + 1 + 1 = 1 (carry of 1)

Question 11

What are the rules for the substraction of binary digits?

Answer 11

• 0 - 0 = 0
• 0 - 1 = 1 (after a borrow)
• 1 - 0 = 1
• 1 - 1 = 0

Question 12

What is the meaning of overflow?

Answer 12

It means the value that has been produced is too large to be stored.

Question 13

An advantage of using two’s complement form

Answer 13

It simplifies the process of substracting one number from another. The number being substracted in converted to its two’s complement form which is then added to the other number

Question 14

What is the use of the binary coded decimal (BCD) scheme?

Answer 14

It is useful in applications that require a single denary digit to be stored or transmitted

Question 15

How does a BCD code represent a denary digit?

Answer 15

Using a nibble

Question 16

What are the two options for the BCD scheme if a denary number with more than one digit is to be converted to BCD

Answer 16

1. Store one BCD in one byte leaving 4 bits unused
2. Packed BCD where 2 4-bit codes are stored in one byte

Question 17

Name 2

Appilcations that use the BCD scheme

Answer 17

1. Denary digits displayed on a screen of a calculator or a digital clock
2. Representation of currency values

Question 18

What is the solution when no needed carry is occured during a BCD arithmetic.

Answer 18

Add 0110