NUMBER SYSTEMS

Question 1

What is a radix?

Answer 1

The base of the number system

Question 2

Explain the prefixes kilo, mega, giga and tera as pertains bits

Answer 2

2^10 = K (kilo),
2^20 = M (mega),
2^30 =G (giga),
2^40 = T (tera).

Question 3

Explain kilobytes, megabytes, gigabytes and terabytes

Answer 3

1 kilobyte (KB) - 1,024 bytes
1 megabyte (MB)- 1,048,576 bytes
1 gigabyte (GB)- 1,073,741,824 bytes
1 terabyte (TB)- 1,099,511,627,776 bytes

Question 4

What are the ways in which signed binary integers may be expressed

Answer 4

 Signed magnitude
 One’s complement
 Two’s complement

Question 5

Describe the signed magnitude way of expressing signed integers. What are its problems?

Answer 5

Left most bit (MSB) is sign bit
 0 means positive
 1 means negative

 Need to consider both sign and magnitude in arithmetic- Signed magnitude representation is easy for people to understand, but it requires complicated computer hardware.
 Two representations of zero (+0 and -0)
 Overflows are discarded

Question 6

What is a minuend and subtrahend

Answer 6

X-Y
X-minuend
Y-subtrahend

Question 7

Describe the one’s complement way of expressing signed integers. What are its problems?

Answer 7

Basically just flipping the bits
 For example, using 8-bit one’s complement representation:
+ 3 is: 00000011
- 3 is: 11111100
 Negative values are indicated by a 1 in the high order bit.
*Carry bit is added to the sum.
*If there is no carry the number is negative

Problems-Two representations of zero (+0 and -0)

Question 8

Describe the one’s complement way of expressing signed integers.

Answer 8

 If the number is positive, just convert it to binary and you’re done.
 If the number is negative, find the one’s complement of the number and then add 1.
+2 = 00000010
+1 = 00000001
+0 = 00000000
-1 = 11111111
-2 = 11111110

Question 9

Do the following operations using both one’s and two’s complement: 12-8 and 8-12

Answer 9

*Do the math babe

Question 10

Describe Binary-Coded Decimal Code

Answer 10

Each group of 4 bits represents one decimal digit.
(185)10 = (0001 1000 0101)BCD = (10111001)2

0- 0000
1- 0001
2- 0010
3- 0011
4- 0100
5- 0101
6- 0110
7- 0111
8- 1000
9- 1001

Question 11

Describe BCD Addition

Answer 11

If the sum is not less than 9 and the carry is not 0 add 6(0110)

*See notes for example

Question 12

Describe Gray Code

Answer 12

 Also known as Reflected Binary Code (RBC)
 2 successive values differ in only 1 bit
 Used to reduce the switching operation of machines

Question 13

Explain the conversion to and from gray code and binary

Answer 13

• See notes

Question 14

What is ASCII in full?

Answer 14

American Standard Code for Information Interchange (ASCII)

Question 15

What is an alphanumeric character set?

Answer 15

a set of elements that includes the 10 decimal digits, the 26 letters of the alphabet, and a number of special characters.

Question 16

How many elements can a set have?

Answer 16

 between 36 and 64 elements - capital letters (six bits)
 between 64 and 128 elements - both uppercase and lowercase letters included (seven bits).

Question 17

Describe ASCII Character Code

Answer 17

 Uses seven bits to code 128 characters
 designated by b1 through b7, with b7 the most significant bit.

-94 graphic characters
 26 uppercase letters (A through Z),
 26 lowercase letters (a through z),
 10 numerals (0 through 9),
 32 special printable characters, such as %, *, and $.
-And 34 control characters are designated in the ASCII
table with abbreviated names eg NUL- null; ACK- acknowledge

*See lecturer material for the ASCII Character Code table

Question 18

Describe the Error‐Detecting Code in ASCII Character Code

Answer 18

 To detect errors, an eighth bit is sometimes added to the ASCII character to indicate its parity.

 A parity bit is an extra bit included with a message to make the total number of 1’s either even or odd.

ASCII A = 1000001
-Even parity- 01000001
-Odd parity- 11000001

ASCII T = 1010100
-Even parity- 11000001
-Odd parity- 01000001