Number Systems & Logic Gates Day 2. Octal Number System Base (Radix)8 Digits0, 1, 2, 3, 4, 5, 6, 7...
-
Upload
regina-peters -
Category
Documents
-
view
219 -
download
0
Transcript of Number Systems & Logic Gates Day 2. Octal Number System Base (Radix)8 Digits0, 1, 2, 3, 4, 5, 6, 7...
Number Systems & Logic GatesDay 2
Octal Number System
Base (Radix) 8
Digits 0, 1, 2, 3, 4, 5, 6, 7
e.g. 16238
1 6 2 3
83=512 8
2=64 8
1=8 8
0=1
The digit 2 in the second position from the right represents the
value 16 and the digit 1 in the fourth position from the right
represents the value 512.
Hexadecimal Number System
Base (Radix) 16
Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
A, B, C, D, E, F
e.g. 2F4D16
2 F 4 D
163=4096 16
2=256 16
1=16 16
0=1
The digit F in the third position from the right represents the
value 3840 and the digit D in the first position from the right
represents the value 13.
Eg. 2210 to Binary
101102
Conversions: Decimal to Binary (Integer)
Remainder
Divide integer until the integer quotient becomes 0
10110
222 5
112222
12 0
Eg. 101102 to Decimal
20 x 021 x 122 x 123 x 024 x 1
16 0 4 2 0+ + + + 22
1 0 1 1 0
Conversions: Binary to Decimal (Integer)
Eg. 13510 to Octal
2078
Conversions: Decimal to Octal (Integer)
07
2
1681358
28
0
Eg. 2078 to Decimal
2 0 780 x 781 x 082 x 2
64 2 0 7+ + 135x
Conversions: Octal to Decimal (Integer)
D
9
3
21116338516
Eg. 338510 to Hexadecimal
F
E
D
12
11
10
-
-
-
15-C
14-B
13-A
D3916
Conversions: Decimal to Hexadecimal (Integer)
1316 0
Eg. D3916 to Decimal
D 3 9 160 x 9161 x 3162 x 13
256 13 48 9+ + 338510x
F
E
D
12
11
10
-
-
-
15-C
14-B
13-A
Conversions: Hexadecimal to Decimal (Integer)
Eg. 110010111012 to Octal
5313
1 1 0 0 1 0 1 1 1 0 1
Conversions: Binary to Octal
Therefore,
110010111012 = 31358
Eg. 31358 to Binary
10101100111
3 1 3 5
Conversions: Octal to Binary
Therefore,
31358 = 110010111012
Eg. 110010111012 to Hexadecimal
D56
1 1 0 0 1 0 1 1 1 0 1
Conversions: Binary to Hexadecimal
Therefore,
110010111012 = 65D16
Eg. 65D16 to Binary
11010101110
6 5 D
Conversions: Hexadecimal to Binary
Therefore,
65D16 = 110010111012
Logic Gates• Binary information is represented in digital
computers by physical quantities called signals.
• Two different electrical voltage levels such as 3 volts and 0.5 volts may be used to represent binary 1 and 0.
• Binary logic deals with binary variables and with operations that assume a logical meaning.
Logic Gates Contd..
• A particular logic operation can be described in an algebraic or tabular form.
• The manipulation of binary information is done by the circuits called logic gates, which are blocks of hardware that produce signals of binary 1 or 0 when input logic requirements are satisfied.
Logic Gates Contd..
• Each gate has a distinct graphics symbol and it’s operation can be described by means of an algebraic expression or in a form of a truth table.
• Each gate has one or more binary inputs and one binary output.
Logic Gates
AND
OR (Inclusive OR)
NOT (inverter)
NAND (Not AND)
NOR (Not OR)
XOR (Exclusive OR)
XNOR (Exclusive NOR)
Logic Operations
ANDLogic Gate Truth Table
A
Bx A B x
0 0 00 1 01 0 01 1 1A, B Binary Input Variables
x Binary Output Variable
X=A.B
Logic Operations
OR Logic Gate Truth Table
A B x0 0 00 1 11 0 11 1 1
A
Bx
X=A+B
This is read as x equals A or B
Logic Operations
NOT Logic Gate Truth Table
A x 0 0 1 1
xA
X=A`
X=A
Logic Operations
NAND Logic Gate Truth Table
A B x0 0 10 1 11 0 11 1 0
A
Bx
X=A.B
Logic Operations
NOR Logic Gate Truth Table
A B x0 0 10 1 01 0 01 1 0
A
Bx
X=A+B
X= A + B
Logic Operations
XOR Logic Gate Truth Table
A B x0 0 00 1 11 0 11 1 0
A
Bx
Logic Operations
Exclusive-NOR
Logic Gate Truth Table
A B x0 0 10 1 01 0 01 1 1
A
Bx
X= A + B