This blog post covers various number system conversions, explaining how to convert numbers between decimal, octal, hexadecimal, and binary representations. The content presents step-by-step procedures for each conversion, making it easy for readers to follow along.
1) Decimal to Octal:
231
231 ÷ 8 = 28
231 % 8 = 7
28 ÷ 8 = 3
28 % 8 = 4
3 ÷ 8 = 0
3 % 8 = 3
So, the octal equivalent of the decimal number 231 is 347.
Octal to Decimal
347
3 * 8^2 + 4 * 8^1 + 7 * 8^0
3 * 64 + 4 * 8 + 7 * 1
192 + 32 + 7 = 231
So, the decimal equivalent of the octal number 347 is 231.
2) Decimal to Hexadecimal
200
200 ÷ 16 = 12
200 % 16 = 8
12 ÷ 16 = 0
12 % 16 = 12 (C)
So, the hexadecimal equivalent of the decimal number 200 is C8.
Hexadecimal to Decimal
C8
C * 16^1 + 8 * 16^0
12 * 16 + 8 * 1
192 + 8 = 200
So, the decimal equivalent of hexadecimal number C8 is 200.
3) Decimal to Binary
125
125 ÷ 2 = 62
125 % 2 = 1
62 ÷ 2 = 31
62 % 2 = 0
31 ÷ 2 = 15
31 % 2 = 1
15 ÷ 2 = 7
15 % 2 = 1
7 ÷ 2 = 3
7 % 2 = 1
3 ÷ 2 = 1
3 % 2 = 1
1 ÷ 2 = 0
1 % 2 = 1
So, the binary equivalent of the decimal number 125 is 1111101.
Binary to Decimal
1111101
= (1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 64 + 32 + 16 + 8 + 4 + 0 + 1
= 125
So, the decimal equivalent of the binary number 1111101 is 125.
