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NPP Number System, Boolean Algebra and Logic Circuits 141

Thus, Binary 1001 is equivalent to decimal AV… ~mBZar g§»`m 1001 Xe_bd g§»`m 9 Ho$
9. This can be symbolically written as: Vwë` h¡ Ÿ& Bgr ~mV H$mo gm§Ho${VH$ ê$n go Bg Vah àX{e©V

{H$`m Om gH$Vm h¡ Ÿ:
(1001) = (9) 10
2
The subscript shows the radix g~pñH«$ßQ> noaoÝWr{gg go {bIr J`r g§»`m go
corresponding to the number written in the gå~pÝYV a¡{S>Šg Xem©Vm h¡Ÿ&
parentheses.
As we have seen in the previous example O¡gm {H$ CnamoŠV CXmhaU _| XoIm J`m h¡ g~go XmE±
that the right most bit was multiplied by 1 and hmW dmbr {~Q> H$mo {g\©$ EH$ go JwUm H$aVo h¢, AV… Bgo
the left most bit was multiplied by 8. Therefore LSB (Least Significant Bit) AWm©V² g~go H$_ ^ma
the right most bit of any binary number is called H$s {~Q> H$hVo h¢ Ÿ& O~{H$ g~go ~mB© dmbr {~Q> H$mo 8 go
Least Significant Bit (LSB) and the Left most
bit is called Most Significant Bit (MSB). The JwUm {H$`m J`m& Bg{bE Bgo MSB (Most Signifi-
diagram Shown below will help in cant bit) `m g~go A{YH$ ^ma dmbr {~Q> H$hVo h¢ Ÿ& ZrMo
remembering the Concept. Xem©E {MÌ H$s ghm`Vm go Bgo `mX aIm Om gH$Vm h¡ Ÿ&
1 0 0 1
↑ ↑
MSB LSB

Memorising the binary equivalents of Xe_bd g§»`mE± 1 go 15 VH$ Ho$ ~mBZar Vwë` `mX
decimal numbers from 1 to 15 is useful. The aIZm ~hþV hr Amdí`H$ h¡ Ÿ& Bgo Vm{cH$m 3.1 _| Xem©`m
following table Shows the equivalents: J`m h¡Ÿ& Bgr Q>o~b Ho$ ZrMo Hw$N> {~Q> Ho$ g_yhm| Ho$ Zm_ {XE

JE h¢Ÿ& BÝh| ^r `mX aIZm Oê$ar h¡Ÿ&
Table 3.1
Decimal Binary Decimal Binary
0 0 8 1000
1 1 9 1001
2 10 10 1010
3 11 11 1011
4 100 12 1100
5 101 13 1101
6 110 14 1110
7 111 15 1111
Sometimes groups of bits are used. 2 bits = G bits (Giga bits) = Gb
30
Following are important: 2 bits = T bits = (Tera bits) = Tb
40
2 2 = 4 bits = Nibble 2 x 8 bits = 1 K Byte (KB)
10
2 3 = 8 bits = Byte 2 x 8 bits = 1 M Byte (MB)
20
2 10 = 1024 bits = Kbits (kilobits) = Kb 2 x 8 bits = 1 G Byte (GB)
30
20
2 bits = M (Mega bits) = Mb 2 x 8 bits = 1 T Byte (TB)
40