4.5.4 Binary Number System Flashcards
Which type of binary can represent -ve numbers? (Signed or Unsigned)
Signed
What is the range of decimal numbers that can be represented using unsigned 4 bit binary?
0 to 15
2^4-1
How many unique bit patterns can be made using 8 bits.
2^8 = 256
Add the unsigned binary integers 1101 and 110
1011 + 110 = 10011 There is no over flow error here since there is no bit restrictions.
Multiply the unsigned binary integers 11001001 and 110
Perform 1 left shift to the original integer so that it becomes 110010010 and then perform two on the original number again and then total them, 1100100100 this totals to 10010110110
011010110110 is a twos compliment signed number with a 8 bit mantissa and a four bit exponent. What is the number in decimal.
The exponent is 0110 which is 6.
Therefore we need to shift the 8 bit number
0.1101011 -> 0110101.1
this is equal to 53.5
Which of these is a twos compliment number:
A) 11010110
B) 01101101
C) 00010101
B, a twos compliment number has to begin with either 01 or 10.
01101101 is a fixed point binary number with four bits after the binary point what is the number in decimal?
0110.1101
The left comes out to 6 and the right is 1/2+1/4+1/16
so it is 6.8125
Convert the number 38.75 into floating point binary with 8 bit mantissa and 4 bit exponent
0100110110110
The decimal point moves 6 points to get
0100110.11 = 38.75
Exponent is 0110 -> 6
Why might fixed and floating point representations of decimal numbers be inaccurate.
Rounding errors can occur in values that cannot be represented exactly by binary.
What type of decimal binary allows for the greatest range of numbers?
Floating Points
Why are floating point numbers normalised?
To provide for a maximum level of precision for a given number of bits.
What error occurs when a number is too large/small to be represented by a given numbers of bits?
Overflow/Underflow
