chapter 1 digital concepts
digital and analog quantities
an analog quantity is one having continuous values. a digital digital quantity is one having a discrete set of values.
binary digits
positive logic: HIGH=1;LOW=0;
negative logic: HIGH=0;LOW=1;
logic levels
in a practical digital circuit, however, a high can be any voltage level between a specified minimum value and a specified maximum value.likewise, a low can be any voltage level between a specified minimum value and a specified maximum value.
no overlap(重叠)
digital waveforms
positive-going pulse: rising edge(leading edge), falling edge(trailing edge)
negative-going pulse:rising edge(trailing edge), falling edge(leading edge)
rise time [fall time]: 10% of the pulse amplitude (height from baseline) to 90%
pulse width: between 50% points
duty cycle(占空比)=pulse width/ the period (T).
chapter 2 number system, operations, and codes
decimal numbers
binary numbers: the weight
binary-to-decimal conversion
decimal-to-binary conversion:
sum- of- weights method----9=8+1=2^3+1
repeated division- by- 2 method----短除法逆序
12/2=6......0
6/2=3......0
3/2=1......1
1/2=0......1
12=1100(B)
converting decimal fraction to binary
0.3125x2=0.625……0
0.625x2= 1.25……1
0.25 x2= 0.50……0
0.50 x2= 1.00……1
(个位)0.3125=.0101(B)
1’s and 2’s complements of binary numbers
finding the 1’s complement: 10110010---->01001101
finding the 2’s complement:
2’s complement=(1’s complement)+1: 10110010---->01001101+1=01001110
signed numbers
a 0 sign bit indicates a positive number, and a 1 sign bit indicates a negative number.
the decimal value of signed numbers
2’s complement
-2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
1 0 1 0 1 0 1 0
=-128+32+8+2=-86
10101010---->11010101+1=11010110=-(64+16+4+2)=-86
range of signed integer numbers that can be represented
range=-(2^(n-1))to (2^(n-1)-1)
floating – point numbers
sign
mantissa: represents the magnitude of the number
exponent: represents the number of paces that the decimal point (or binary point ) is to be moved.(指数)
single-precision -->s(1bit)—exponent(8 bits)—mantissa(23 bits) [32 bits]
double-precision—>s(1 bit)—exponent(11 bits)—mantissa(52 bits) [64 bits]
there are 24 bits(single precision) in the mantissa because in any binary number the left-most bit is always a 1. therefore , this 1 is understood to be there although it does not occupy an actual bit position.
1011010010001=1.011010010001x 2^12
s=0,e=10001011=139=127+12,mantissa=01101001000100000000000
exponent-127
arithmetic operations with signed numbers
addition
both numbers positive: 00000111+00000100=00001011—>7+4=11
positive number with magnitude larger than negative number:00001111+11111010=1 00001001 (15-6=9)
negative number with magnitude larger than positive number:00010000+11101000=11111000 (16-24=-8)
both numbers negative:11111011=11110111=1 11110010 (-5-9=-14)
overflow condition(only occur when both numbers are positive or negative )
01111101+00111010=10110111 (125+58=183)
subtraction
the sign of a positive or negative number is changed by taking 2’s complement
00000100(+4) 11111100(-4)
multiplication
the partial method is perhaps the more common one because it reflects the way you multiply longhand.
step1—sign
step2—change any negative number to true(uncomplemented) form.
step3—generate the partial products(only the magnitude bits are used in these steps)
step4—add each partial products
step5—if sign that was determined is negative, 2’s complement,if positive ,attach the sign bit to the product.
division
dividend / divisor =quotient
subtract the divisor
hexadecimal numbers
binary code decimal
原文：https://www.cnblogs.com/feishijieqiusheng/p/12830290.html