Digital System Tasks


Converting Decimal Numbers to Binary Numbers and contrast
– Conversion Decimal To Binary
a. 39 / 2 = 19 remainder 1 (Least significant digit (LSB)
19 / 2 = 9 remainder 1
9 / 2 = 4 remainder 1
4 / 2 = 2 remainder 0
2 / 2 = 1 remainder 0
So 3910 = 10,011,102

b. 0,2510
– 0.25 x 2 = 0:50 remaining 0 (MSB)
0.50 x 2 = 1.00 remaining 1
0.00 x 2 = 0.00 remainder 0 (LSB)
So 0.2510 = 0.0102

– Converting Binary Numbers to Decimal Numbers

c. 111010012 = 1 × 23 0 × 22 0 × 21 1 × 20
= 0 8 0 1 = 910
So 111 012 = 910

d. 1111.012 = 1×23 1×22 1 × 21 1 × 20 0 × 2-1 1 × 2-2
= 8 4 2 1 0 0.25
= 15, 2510
Converting Decimal Numbers to Octal Numbers and vice versa
Converting Decimal Numbers to Octal Numbers
1. 30510
– 702 / 8 = 87 remainder 1 (LSB)
– 87 / 8 = 6 remainder 6
– 10 / 8 = 1 remainder 1 (MSB)
– 1 / 8 = 0 remainder 1
= 1168
b. 0,310
– 0.4 x 8 = 3.2 the remaining 3 (MSB)
– 0.2 x 8 = 1.6 remaining 1
– 0.6 x 8 = 4.8 the remaining four
– 0.8 x 8 = 6.4 the remaining 6 (LSB)

0,410 = 0.31468
Converting Octal Numbers to Decimal Numbers

c. 2818 = 2 × 82 8 × 81 1 × 80
= 128 1
= 12 910
d. 115.48 = 1×82 1 × 81 5 × 80 4 × 8-1
= 29.510

Converting Decimal Numbers to Hexadecimal Numbers
– Convert Hexadecimal to Decimal
a. 132 116 = 1×163 3 x 162 2 × 161 1 × 80
= 4096 768 32 1
= 489 710
b. 0.216 = 0 × 160 2 × 16-1
= 0 .32
= 0.3210
Converting Decimal to Hexadecimal

1. 0.2510 = 0.25 x 16 = 4.00 the remaining 4 (MSB)
= 0.00 x 16 = 0.00 remainder 0 (LSB)
= 0.4016

2. 32510 = 325 / 16 = 20 remainder 5 (LSB)
= 20/16 = 1 remainder 4
= 1 / 16 = 0 remainder 1 (MSB)
= 14 516

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