Binary Number System

Question 1

What is signed binary?

Answer 1

Signed binary numbers are encoded to include a positive or negative sign.

Question 2

What is unsigned binary?

Answer 2

Unsigned binary numbers do NOT have a positive or negative sign so are useful for positive whole numbers only.

Question 3

What is the advantage of using unsigned binary?

Answer 3

The advantage of using unsigned integers is that they can be used to store larger numbers than using signed integers

Question 4

What minimum and maximum value does unsigned binary have?

Answer 4

An unsigned binary number has a minimum of zero and a maximum value of 2n-1,

Question 5

What is the binary addition rules?

Answer 5

Binary Addition Rules:
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 102 write down 0 and carry 1
1 + 1 + 1 = 112 write down 1 and carry

Question 6

How would you add the binary numbers 0111 and 0101 ?

Answer 6

1 + 1 = 2 so write 0 and carry 1
1 + 0 + 1 = 10 binary so write 0 and carry 1
1 + 1 + 1 = 11 binary so write 1 and carry 1
0 + 0 + 1 = 1 binary so write 1
So 0111 + 0101 = 1100 binary

Question 7

What are the rules for binary mutliplication?

Answer 7

Binary Multiplication Rules:
0 x 0 = 0
1 x 0 = 0
0 x 1 = 0
1 x 1 = 1 (there are no carry or borrow bits with binary multiplication)

Question 8

How would you multiply binary numbers 0011011 by 101 ?

Answer 8

Multiply 0011011
By 101
Step 1 multiply 00011011 by 1

Step 2 multiply 00011011 by 1 and shift 2 places
Binary addition three rows for final answer
Use carry bits where necessary
So 00011011 x 00000101 = 10000111 binary