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Express the hexadecimal integer $AB12F$ in binary (easy) and in decimal (harder).

An archived instance of discourse for discussion in undergraduate Real and Numerical Analysis.

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Express the hexadecimal integer $AB12F$ in binary (easy) and in decimal (harder).

Cheryl

$AB12F$ is represented in binary as $$1010 | 1011 | 0001 | 0010 | 1111$$ very simple, any binary number from $10-15$ are represented as letters $A-F$.

Cheryl

Hex to decimal is only a little harder arithmetic wise. Just remember that you are working in base 16 and indexing the number from right to left, starting at zero. $$AB12F_{16}=A*16^4+B*16^3+1*16^2+2*16^1+F*16^0$$

$$=(10*65536)+(11*4096)+(1*256)+(2*16)+(15*1)$$

$$=700719$$

amccann1

0xAB12F

Binary: 1010 1011 0001 0010 1111

Decimal: 2^19 + 2^17 + 2^15 + 2^13 + 2^12 + 2^8 + 2^5 + 2^3 + 2^2 + 2^1 + 2^0 = 700,719