Higher Engineering Mathematics

COMPUTER NUMBERING SYSTEMS 91

A

(b) BD 16 =B× 161 +D× 160

= 11 × 16 + 13 × 1 = 176 + 13 = 189

ThusBD 16 = (^18910)
Problem 13. Convert 1A4E 16 into a denary
number.
1A4E 16 = 1 × 163 +A× 162 + 4 × 161 +E× 160
= 1 × 163 + 10 × 162 + 4 × 161

• 14 × 160
  = 1 × 4096 + 10 × 256 + 4 × 16 + 14 × 1
  = 4096 + 2560 + 64 + 14 = 6734
  Thus1A4E 16 = (^673410)
  To convert from decimal to hexadecimal
  This is achieved by repeatedly dividing by 16 and
  noting the remainder at each stage, as shown below
  for 26 10.
  26
  110
  0 1
  A 16
  (^116)
  most significant bit 1 A
  Remainder
  least significant bit
  16
  16
  Hence 2610 =1A 16
  Similarly, for 447 10
  44716
  15
  11
  F 16
  B 16
  1 F
  Remainder
  27
  1
  0
  16
  16
  (^1116)
  B
  Thus 44710 =1BF 16
  Problem 14. Convert the following decimal
  numbers into their hexadecimal equivalents:
  (a) 37 10 (b) 108 10
  3716
  16 2
  0
  5 = (^516)
  2 = (^216)
  most significant bit
  2 5
  Remainder
  least significant bit
  (a)
  Hence 3710 = (^2516)
  16 108 Remainder
  16 6 12 = C 16
  0 6 = 6 16
  6 C
  (b)
  Hence 10810 =6C 16
  Problem 15. Convert the following decimal
  numbers into their hexadecimal equivalents:
  (a) 162 10 (b) 239 10
  16 162 Remainder
  16 10 2 = 2 16
  0 10 = A 16
  A 2
  (a)
  Hence 16210 =A2 16
  16 239 Remainder
  16 14 15 = F 16
  0 14 = E 16
  E F
  (b)
  Hence 23910 =EF 16
  To convert from binary to hexadecimal:
  The binary bits are arranged in groups of four, start-
  ing from right to left, and a hexadecimal symbol