DIGITAL FUNDAMENTALS, SPRING 25 - EXAM III |
WITH COMPLETE SOLUTION!!
Binary Counters Answer - Group of flip-flops connected in a special
arrangement in which the states of the flip-flops represent the binary number
equivalent to the number of pulses that have occurred at the input of the
counter
Signed Answer - Binary bit that is added to the leftmost position of a binary
number to indicate whether that number represents a positive or a negative
quantity.
- Negative = MSB
Sign Bit: 0 = positive, 1= negative
Sign-magnitude system --Example : 52 (decimal) = 1101002 (binary)
+ 52 = 01101002 (sign-magnitude)
- 52 = 11101002 (sign-magnitude)
Unsigned Answer - - Unsigned numbers are always non-negative numbers. 0 -
255
Positive = MSB
Range of values Answer - Unsigned = 0 - 255
Signed = -128 to +127
,Negation Answer - Negation is the operation of converting a positive number
to its negative equivalent or a negative number to its positive equivalent.
- Start with 00001001 = 9
- 2's complement (negate) 11110111 = -9
- negate again 00001001 = 9
Carried Out Flag Answer - Carry — Digit or bit that is generated when two
numbers are added and the result is greater than the base for the number
system being used.
Carry Propagation — Intrinsic circuit delay of some parallel adders that
prevents the carry bit (COUT) and the result of the addition from appearing at
the output simultaneously.
Carry Ripple — See Carry Propagation.
Over flow flag Answer - Occur only when two positive or two
negative numbers are being added, and it always produces an incorrect result.
When in the process of adding signed binary numbers, a carry of 1 is generated
from the MSB position of the number into the sign bit position.
Arithmetic Overflow Answer - - Overflow Condition: » Two positive or two
negative numbers are being added
- Overflow Detection: » Detected by observing the carry into the sign bit
position and the carry out of the sign
bit position. » If these two carries are not equal,
an overflow condition is produced
, 2's Compliment (Adding and Subtracting) Answer - The 2's complement of a
binary number is formed by taking the 1's complement
of the number and adding 1 to the least-significant-bit position. The
process is illustrated below for 101101^2 = 45^10. 101101 (binary of 45).
010010 = complement each bit to form 1's complement. +1 = add 1 to form 2's
compliment. 010011 = 2's complement of original binary number.
When result is too big: 2 Flags
1) Unsigned: carried = set = result too big to fit
2) Signed = Overflow flat (V, OFL)= result too big to fit
Fix Point Format Answer - Have a constant number of digits after the decimal
place. These are typically used to represent money, percentages, or a certain
precision of the number of seconds (i.e. limiting to milliseconds). They are
mostly used in databases as a simple and efficient storage format. The math
involved with these types of numbers have no practical significance for any
precision lower than the fixed number of decimal places.
Floating Point format Answer - Within the limits of the binary representation,
floating point numbers represent arbitrary precision. In short, you can
represent really tiny numbers or really big numbers. The number of decimal
places you can represent are only limited by the number of bits dedicated to
the number. These are commonly used in physics and other more precise math
problems.
Adding Binary Answer - Only four[4] cases can occur in adding the two binary
digits (bits) in any position.
1) 0+0 = 0
2) 1+0 = 1
3) 1+1 = 10 = 0+ carry 1 into next position.
4) 1+1+1 = 11 = 1 + carry 1 into next position.
WITH COMPLETE SOLUTION!!
Binary Counters Answer - Group of flip-flops connected in a special
arrangement in which the states of the flip-flops represent the binary number
equivalent to the number of pulses that have occurred at the input of the
counter
Signed Answer - Binary bit that is added to the leftmost position of a binary
number to indicate whether that number represents a positive or a negative
quantity.
- Negative = MSB
Sign Bit: 0 = positive, 1= negative
Sign-magnitude system --Example : 52 (decimal) = 1101002 (binary)
+ 52 = 01101002 (sign-magnitude)
- 52 = 11101002 (sign-magnitude)
Unsigned Answer - - Unsigned numbers are always non-negative numbers. 0 -
255
Positive = MSB
Range of values Answer - Unsigned = 0 - 255
Signed = -128 to +127
,Negation Answer - Negation is the operation of converting a positive number
to its negative equivalent or a negative number to its positive equivalent.
- Start with 00001001 = 9
- 2's complement (negate) 11110111 = -9
- negate again 00001001 = 9
Carried Out Flag Answer - Carry — Digit or bit that is generated when two
numbers are added and the result is greater than the base for the number
system being used.
Carry Propagation — Intrinsic circuit delay of some parallel adders that
prevents the carry bit (COUT) and the result of the addition from appearing at
the output simultaneously.
Carry Ripple — See Carry Propagation.
Over flow flag Answer - Occur only when two positive or two
negative numbers are being added, and it always produces an incorrect result.
When in the process of adding signed binary numbers, a carry of 1 is generated
from the MSB position of the number into the sign bit position.
Arithmetic Overflow Answer - - Overflow Condition: » Two positive or two
negative numbers are being added
- Overflow Detection: » Detected by observing the carry into the sign bit
position and the carry out of the sign
bit position. » If these two carries are not equal,
an overflow condition is produced
, 2's Compliment (Adding and Subtracting) Answer - The 2's complement of a
binary number is formed by taking the 1's complement
of the number and adding 1 to the least-significant-bit position. The
process is illustrated below for 101101^2 = 45^10. 101101 (binary of 45).
010010 = complement each bit to form 1's complement. +1 = add 1 to form 2's
compliment. 010011 = 2's complement of original binary number.
When result is too big: 2 Flags
1) Unsigned: carried = set = result too big to fit
2) Signed = Overflow flat (V, OFL)= result too big to fit
Fix Point Format Answer - Have a constant number of digits after the decimal
place. These are typically used to represent money, percentages, or a certain
precision of the number of seconds (i.e. limiting to milliseconds). They are
mostly used in databases as a simple and efficient storage format. The math
involved with these types of numbers have no practical significance for any
precision lower than the fixed number of decimal places.
Floating Point format Answer - Within the limits of the binary representation,
floating point numbers represent arbitrary precision. In short, you can
represent really tiny numbers or really big numbers. The number of decimal
places you can represent are only limited by the number of bits dedicated to
the number. These are commonly used in physics and other more precise math
problems.
Adding Binary Answer - Only four[4] cases can occur in adding the two binary
digits (bits) in any position.
1) 0+0 = 0
2) 1+0 = 1
3) 1+1 = 10 = 0+ carry 1 into next position.
4) 1+1+1 = 11 = 1 + carry 1 into next position.
