BITS,BINARY AND LOGIC
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Transcript of BITS,BINARY AND LOGIC
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CLICK HERE
Welcome To Our Courseware
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LOADING…….
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FLOATING POINT
1’s & 2’s Complimen
t
LOGIC OPERATIONS
HEXADECIMAL
E-LEARNING CENTER
CONVERTING
CHOOSE YOUR TOPIC
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CONVERTING
Binary to Decimal
Decimal to Binary
Binary to Hexadecimal
CHOOSE YOUR TOPIC
MAIN MENU
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LOGIC OPERATIONS
AND GATE
ADDITION
OR GATE
SUBRACTION
CHOOSE YOUR TOPIC
MAIN MENU
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0 0111 100
UNSIGNED INTEGER
CONVERTING LOGIC OPERATION EXITMAIN MENU
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1’S COMPLIMENT
L PIF 0 0111 100
UNSIGNED INTEGER
CONVERTING LOGIC OPERATION EXITMAIN MENU
CLICK HERE TO 2’COMPLIMENT
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11 100
+
1’S COMPLIMENT
2’S COMPLIMENT
0 011UNSIGNED INTEGER
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0 1 1 0
2023
22 21
Mostsignificant
Leastsignificant
n 2n
0 1
1 2
2 4
3 8
4 16
5 32
6 64
7 128
8 256
9 512
10 1024
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1 1
=
2023 22 21 +++
4 2+
6=
0 0
0 1 1 0
202322 21
ONLY 1 (CIRCLE) WAS COUNT
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663
22
01
12 1
00110
READ FROM DOWN TO UP
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1 010
0 100+SIGNED
INTEGER
ANSWER
1 100SIGNED INTEGER
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10 010
+
1’S COMPLIMENT
2’S COMPLIMENT
1 101NEGATIVE INTEGER
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1 0001 011
-1
ANSWER
1 1005
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1 0111 011
OR
ANSWER
1 010
ORuseful for setting bitsOR with zero = no changeOR with one = 1
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1 0001 000
AND
ANSWER
1 110
ANDuseful for clearing bitsAND with zero = 0AND with one = no change
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• It is often convenient to write binary (base-2) numbersas hexadecimal (base-16) numbers instead.– fewer digits -- four bits per hex digit– less error prone -- easy to corrupt long string of 1’s
and 0’s
HEXADECIMAL NOTATION
CONVERTING LOGIC OPERATION EXITMAIN MENU
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Binary Hex Decimal
0000 0 0
0001 1 1
0010 2 2
0011 3 3
0100 4 4
0101 5 5
0110 6 6
0111 7 7
Binary Hex Decimal
1000 8 8
1001 9 9
1010 A 10
1011 B 11
1100 C 12
1101 D 13
1110 E 14
1111 F 15
HEXADECIMAL NOTATION
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Every four bits is a hex digit.– start grouping from right-hand side– Is refer to hexamdecimal table
1101 0001 1010 1111
FA1D
HEXADECIMAL NOTATION
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• Large values: 6.023 x 1023 -- requires 79 bits• Small values: 6.626 x 10-34 -- requires >110 bits
• Use equivalent of “scientific notation”: F x 2E
• Need to represent F (fraction), E (exponent), and sign.• IEEE 754 Floating-Point Standard (32-bits):
S Exponent Fraction
1b 8b 23b
0exponent,2fraction.0)1(
254exponent1,2fraction.1)1(126
127exponent
S
S
N
N
FLOATING POINT
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00101000.101 (40.625)
+ 11111110.110 (-1.25)
00100111.011 (39.375)
2-1 = 0.52-2 = 0.252-3 = 0.125
How can we represent fractions?Use a “binary point” to separate positivefrom negative powers of two -- just like “decimal point.”2’s comp addition and subtraction still work.
if binary points are aligned
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2-22
Single-precision IEEE floating point number:
1 01111110 10000000000000000000000
sign exponent fractionSign is 1 – number is negative.Exponent field is 01111110 = 126 (decimal).Fraction is 0.100000000000… = 0.5 (decimal).
Value = -1.5 x 2(126-127) = -1.5 x 2-1 = -0.75.
FLOATING POINT
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Thank you, see you again