Binary number system In digital electronics we only

Binary number system In digital electronics, we only deal with 2 voltage levels (High or Low; On or OFF), for this reason, almost all digital systems use the binary (base 2) number system as the system of its operations.

Binary number system Binary number are strings of two (hence ‘bi’), symbols 0’s and 1’s, that represent numbers. They may be expanded in the usual way with a base of 2. E. g. 11012 20 21 22 23 1 0 4 8 + 1310 Click TO Continue

Binary number system Ø Each digit in the binary number system is called a bit Ø A group of four bits binary number is known Nibble. Ø A group of eight bits binary number is known as Byte. Ø Two bytes number form a word.

Binary – to – decimal conversion Whole number Convert 111012 to decimal number 110112 = (1)*24 + (1)*23 + (1)*22 + (0)*21 + (1)*20 = 1*16 + 1*8 + 1*4 + 0*2 + 1*1 = 16 +8 +4 +0 +1 = 2910 Click TO Continue

Try the following Convert 101102 to decimal number Solution 101102 = (1)*24 + (0)*23 + (1)*22 + (1)*21 + (0)*20 = 1*16 + 0*8 + 1*4 + 1*2 + 0*1 = 16 +0 +4 +2 +0 = 2210 Click For Solution

Binary – to – decimal conversion Fraction number Convert 1012 to decimal number 1012 = (1)*22 + (0)*21 + (1)*20 + (1)*2 -1 + (0)*2 -2 + (1)*2 -3 = 1*4 + 0*2 + 1*0. 5 + 0*0. 25 +1*0. 125 =4 +0 +1 + 0. 5 +0 + 0. 125 = 5. 62510 Click TO Continue

Try the following Convert 110. 112 to decimal number Solution 110. 112 = (1)*22 + (1)*21 + (0)*20 + (1)*2 -1 + (1)*2 -2 =4 +2 + 0. 5 + 0. 25 = 6. 7510 Click For Solution

Decimal – to – binary conversion Whole number Convert 2510 to decimal number by repeated division 2 2 2 Click TO Continue 25 12 6 3 1 0 Remainder 1 LSB 0 0 1 1 MSB 2 510 = 1 1 0 012

Try the following Convert 3010 to binary number Solution 2 2 2 Click For Solution 30 15 7 3 1 0 Remainder 0 1 1 Ans = 111102

Decimal – to – binary conversion Fraction number Convert 0. 37510 to decimal number by repeated multiplication Carry 0. 375 x 2 = 0. 75 0 0. 75 x 2 = 0. 5 1 0. 37510 0. 5 1 = 0. 0112 Click TO Continue x 2= 0

Try the following Convert 13. 12510 to binary number Solution Whole number 2 2 Click For Solution 13 6 2 3 2 1 2 0 Fraction number Carry Remainder 1 0 1 1 0. 125 x 2 = 0. 25 0 0. 25 x 2 = 0. 5 0 0. 5 1 x 2= 0 Ans = 1101. 0012