1. Convert the following binary number to octal, hexadecimal, BCD, and decimal (

Question

1. Convert the following binary number to octal, hexadecimal, BCD, and decimal (5 - 10points) 1001011001010011 Octal Hexadecimal BCD decimal Prep: Be able to convert binary to Octal,Hex, BCD& Decimal; also decimal to Octal, Hex, BCD& Decimal 2. Conert the decimal number -s to 16 bit signed binary, Is complement, and 2s complement (5 points) -5 signed binary Is complement 2s complement Prep: Know how to form complements (1s, 2s, 9s,10s) 3. Sum the following BCD numbers: 25 + 17 (10 points) 00100101 0001 0111 Prep: Be able to add or subtract 2, binary or BCD numbers 4. State absorption Theorems a &b; using x & y ( 10points) Prep: Be able to state Basic Theorems using symbols 5a. Simplify the following Boolean functions TI the logie diagram: (20-30 points) A B CTI T2 0 0 01 0 TI- Prep: Be able to develop logic functions from truth table & draw logie diagram.

Explanation / Answer

1)

Binary to decimal conversion:

For Binary to decimal conversion we multiply the each bits of binary number by 2 to the power of position of that bit and all the decimal values of each bit.

1001011001010011 number has 16 bits so we multiply each bit by 2 to the power of position of that bit and all the decimal values.

(1001011001010011)2 = [(1 x 215) + ( 0 x 214) + ( 0 x 213) + (1 x 212) + ( 0 x 211) + ( 1 x 210) + ( 1 x 29) + (0 x 28) + (0 x 27) + ( 1 x 26) + ( 0 x 25) + ( 1 x 24) + ( 0 x 23) + ( 0 x 22) + ( 1 x 21) + (1 x 20)]

=[ ( 1 x 32768) + 0 + 0 + ( 1 x 4096) + 0 + ( 1 x 1024) + (1 x 512) + 0 + 0 + (1 x 64) + 0 + ( 1 x 16) + 0 + 0 + ( 1 x 2) + ( 1 x 1 )]

=[ 32768 + 4096 + 1024 + 512 + 64 + 16 + 2 + 1]

= (38483)10

Binary to Octal

For Binary to octal we divide them into group of 3 bits and write their octal values

(1001011001010011)2 = 001 001 011 001 010 011

= 1 1 3 1 2 3

= (1 1 3 1 2 3)8

For Binary to Hexadecimal we divide the number into group of 4 bits and write their hexadecimal values of each 4 bit as hexadecimal can have 16 values( i.e, maximum 4 bits)

(1001011001010011)2 = 1001 0110 0101 0011

= 9 6 5 3

= (9653)16

Binary to BCD

For Binary to BCD

a) First the decimal value of binary number is calculated.

Here we hace calculated decimal value as (38483)10

b) Convert the each digit of decimal number into 4 bit binary value to get BCD value.

Here,

3 - 0011

8 - 1000

4 - 0100

3 8 4 8 3 = 0011 1000 0100 1000 0011

= ( 00111000010010000011)BCD

(1001011001010011)2   = ( 00111000010010000011)BCD

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