Conversions: Decimal to Binary, Binary to Decimal, Binary to Hex, Hex to Decimal, Study notes of Computer Architecture and Organization

Instructions for converting decimal numbers to binary and hexadecimal, as well as binary and hexadecimal numbers to decimal. It includes examples of each conversion process.

Typology: Study notes

Pre 2010

Uploaded on 02/25/2010

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A Quick Review
zDecimal to binary
zBinary to decimal
zBinary to hexadecimal
zHexadecimal to binary
zHexadecimal to Decimal
zBinary addition
zBinary subtraction
zBinary shift
Decimal to Binary
z146d = ????????b
z146/2 = 73 Remainder = 0 LSB (73)
z73/2 = 36 Remainder = 1 (36.5)
z36/2 = 18 Remainder = 0 (18)
z18/2 = 9 Remainder = 0 (9)
z9/2 = 4 Remainder = 1 (4.5)
z4/2 = 2 Remainder = 0 (2)
z2/2 = 1 Remainder = 0 (1)
z1/2 = 0 Remainder = 1 MSB (0.5)
z146d = 10010010b
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A Quick Review

zDecimal to binary

zBinary to decimal

zBinary to hexadecimal

zHexadecimal to binary

zHexadecimal to Decimal

zBinary addition

zBinary subtraction

zBinary shift

Decimal to Binary

z 146d = ????????b z 146/2 = 73 Remainder = 0 LSB (73) z 73/2 = 36 Remainder = 1 (36.5) z 36/2 = 18 Remainder = 0 (18) z 18/2 = 9 Remainder = 0 (9) z 9/2 = 4 Remainder = 1 (4.5) z 4/2 = 2 Remainder = 0 (2) z 2/2 = 1 Remainder = 0 (1) z 1/2 = 0 Remainder = 1 MSB (0.5) z 146d = 10010010b

Binary to Decimal

z10010010b = ???d

zWhich positions have ones?

{7, 4 and 1

z12^7 + 12^4 + 1*2^1 = 128 + 16 + 2 = 146

Binary to Hexadecimal

z10010010b = ??h

zSplit binary string into 4 bit components

z1001b = 9d = 9h

z0010b = 2d = 2h

zConcatenate the hex digits

z10010010b = 92h

Binary Addition

z 1+1 = 10 (carry 1)

z 0+1 = 1

z 1+0 = 1

z 0+0 = 0

z 1+1+1=11 (carry 1)

Binary Subtraction

z 1-1 = 0

z 1-0 = 1

z 0-1 = 1 (borrow)

z 0-0 = 0

z *) borrow

Multiplication and Division by Shifting

(Optimization trick)

z0001010b = 10d

zShift left (multiply by 2)

{0010100b = 20d {0101000b = 40d

zShift right (divide with 2)

{0000101b = 5d (remainder 0 shifted out) {0000010b = 2d (remainder 1 shifted out)

Calculating Two Complement

z58d = 00111010b

z-58d = TC(58d) = TC(00111010b) =?

zOne complement

{OC(00111010b) = 11000101b

zAdd one

z-58d = 11000110b 11000110

Two Complement Addition

z48d + (-58d) = -10d

z48d = 00110000b

z-58d = TC(58d) = 11000110b

z-10d = TC(10d) = 11110110b