Test 1 Flashcards
The unsigned binary range for six bit cell:
000000 to 11 1111 .
0-63
(2^n )-1
In fractional values the quantity 1/2 exactly representable in the binary and decimal systems, but is not in the _________ numbering system .
Ternary Base 3
Fractional decimal values have __________ to the right of the decimal point.
nonzero digits
Fractional values of other radix systems have nonzero digits to the:
Right if the radix point
Numerals to the right of a radix point represent:
Negative powers of the radix
As with whole-number conversions, you can use either of two methods:
a subtraction method or an easy multiplication methods
The subtraction method for fractions is identical to the subtraction method for whole numbers. Instead of subtracting positive powers of the target radix, we:
subtract negative powers of the radix.
We always start with the largest value first ______ where ___ is our radix, and work our way along using larger negative exponents.
n^-1
n
When adding two binary numbers , it is possible for each number to be in the range for the number of bits in the storage cell but for their sum to be out of range.
Carry bit
To represent signed integers, computer systems allocate the ______ bit to indicate the sign of a number
high -order
The _______ bit is the leftmost bit. It is also called the most significant bit.
High-order
There are three ways in which signed binary integers may be expressed:
Signed magnitude
One’s complement
Two’s complement
In an 8-bit word, ___________ representation places the absolute value of the number in the 7 bits to the right of the sign bit.
Signed magnitude
Signed magnitude representation is easy for people to understand, but it requires:
complicated computer hardware because you have to hardware for adding and subtracting .
Another disadvantage of signed magnitude is that it allows:
two different representations for zero : positive zero and negative zero .
Two representations for zero are reasons (among others ) computers systems employ _____________ for numeric value representation .
complement systems
In complement systems, negative values are represented by some difference
between a number and its base .
The ____________ of a non zero number N in base r with d digits is (r^ d; 1)-N
diminished radix complement
_____________ are useful because they eliminate the need for subtraction. The difference of two values is found by adding the minuend to the complement of the subtrahend.
Complement systems
One’s complement is simpler to implement than
signed magnitude.
But ___________ still has the disadvantage of having two different representations for zero : positive zero and negative zero. ___________ solves this problem.
Ones complement
Twos complement
___________ is the radix complement of the binary numbering system; the radix complement of a non- zero number N in base r with d digits is r ^ d - N
Two’s complement
With twos complement:
If the number is positive:
If the number is negative:
just convert it to binary and you’re done .
find the one’s complement of the number and then add 1 .
In 8 bit binary, 3 is:
- 3 In ones complement:
- 3 In twos complement:
0000 0011
1111 1100
1111 1101
Range for signed binary integers
1111 to 0111
-7 to 7
Range for ones complement
1000 to 0111
-7 to 7
Range for twos complement
1000 to 0111
-8 to 7
When we use any finite number of bits to represent a number, we always run the risk of.
the result of our calculations becoming too large or too small to be stored in the computer
While we can’t always prevent overflow , we can always ______ overflow.
Detect
In complement arithmetic , an overflow condition is ____ to detect.
Easy
Status bits:
N = 1 N = 0 Z = 1 Z = 0 V = 1 V = 0 C = 1 C = 0
Neg Otherwise Result is all zeros Otherwise Signed internet overflow Otherwise And unsigned integer overflow Otherwise
The purpose of ____________ is to specify precisely the effect of a hardware operation .
Register Transfer Language (RTL)
